0. Review of Algebra

Multiplying Polynomials

0. Review of Algebra

Multiplying Polynomials

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Multiply Polynomials Using the Distributive Property

Special Products - Square Formulas

Special Products - Cube Formulas

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How to Multiply Polynomials Properly - Nerdstudy

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How to Multiply Polynomials Properly - Nerdstudy

Multiplying Polynomials - Math Tutorial

Multiplying Polynomials

Use FOIL Method to Multiply Polynomials Algebra

Special Polynomial Products

GreeneMath.com

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Multiple Choice

Multiply the polynomials using FOIL.

$\left(x-5\right)\left(x-12\right)$

Multiply the polynomials using FOIL.

$\left(4x+7\right)\left(-x+6\right)$

Multiply the polynomials using FOIL.

$\left(x^2-3x\right)\left(2x+8\right)$

Multiply the polynomials.

$\left(x+4\right)\left(3x^2-2x+1\right)$

Multiply the polynomials.

$\left(x+3\right)\left(x-5\right)\left(-2x+1\right)$

Multiply the polynomials using special product formulas.

$\left(5x-9\right)\left(5x+9\right)$

Multiply the polynomials using special product formulas.

$\left(3x+5\right)\left(3x+5\right)$

Multiply the polynomials using special product formulas.

$\left(2x+4\right)^3$

In Exercises 1–8, multiply the monomials. (3x²)(5x⁴)

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Textbook Question

In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 2x+3x^2−5

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Textbook Question

Evaluate each algebraic expression for the given value or value(s) of the variable(s). 3+6(x-2)^3 for x=4

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Textbook Question

In Exercises 1–4, is the algebraic expression a polynomial? If it is, write the polynomial in standard form. (2x+3)/x

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Textbook Question

Fill in the blank to correctly complete each sentence. In the term -6x^2y, -6 is the ______.

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Textbook Question

In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x−1)/(x^2+11x+10)

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Textbook Question

In Exercises 5–8, find the degree of the polynomial. x^2−4x^3+9x−12x^4+63

In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (3x−9)/(x^2−6x+9)

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Textbook Question

In Exercises 9–22, multiply the monomial and the polynomial. 4x²(3x+2)

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Textbook Question

In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (y^2+7y−18)/(y^2−3y+2)

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Textbook Question

In Exercises 9–22, multiply the monomial and the polynomial. 2y(y²−5y)

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Textbook Question

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these.See Example 1. -5x^11

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Textbook Question

In Exercises 9–22, multiply the monomial and the polynomial. 5x³ (2x⁵−4x²+9)

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Textbook Question

In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (5x^2−7x−8)+(2x^2−3x+7)−(x^2−4x−3)

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Textbook Question

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these.See Example 1. 6x+3x^4

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Textbook Question

In Exercises 7–14, simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression. (x^2−14x+49)/(x^2−49)

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Textbook Question

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these.See Example 1. -7z^5-2z^3+1

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Textbook Question

In Exercises 15–58, find each product. (x+1)(x^2−x+1)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (6x+9)/(3x−15) ⋅ (x−5)/(4x+6)

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Textbook Question

In Exercises 15–58, find each product. (2x−3)(x^2−3x+5)

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Textbook Question

In Exercises 15–58, find each product. (x+7)(x+3)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (x^3−8)/(x^2−4) ⋅ (x+2)/3x

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Textbook Question

Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these.See Example 1. 5

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Textbook Question

In Exercises 9–22, multiply the monomial and the polynomial. −4xⁿ (3x²ⁿ − 5xⁿ + 1/2 x)

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Textbook Question

In Exercises 23–34, find each product using either a horizontal or a vertical format. (x−3)(x²+2x+5)

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Textbook Question

Add or subtract, as indicated. See Example 2. (5x^2-4x+7) + (-4x^2+3x-5)

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Textbook Question

Add or subtract, as indicated. See Example 2. (3m^5-3m^2+4) + (-2m^3-m^2+6)

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Textbook Question

In Exercises 23–34, find each product using either a horizontal or a vertical format. (x−1)(x²+x+1)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x−2) ÷ (x+2)/(4x−8)

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Textbook Question

In Exercises 15–58, find each product. (2x−5)(7x+2)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (x^2+x)/(x^2−4) ÷ (x^2−1)/(x^2+5x+6)

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Textbook Question

In Exercises 15–58, find each product. (7x^2−2)(3x^2−5)

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Textbook Question

In Exercises 15–58, find each product. (7x^3+5)(x^2−2)

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Textbook Question

Find each product. See Examples 3–5. (5m-6)(3m+4)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (x^2−4)/(x^2+3x−10) ÷ (x^2+5x+6)/(x^2+8x+15)

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Textbook Question

Find each product. See Examples 3–5. x^2(3x-2)(5x+1)

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Textbook Question

In Exercises 15–32, multiply or divide as indicated. (x^3−25x)/4x^2 ⋅ (2x^2−2)/(x^2−6x+5) ÷ (x^2+5x)/(7x+7)

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Textbook Question

Find each product. See Examples 3–5. 4x^2(3x63+2x^2-5x+1)

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Textbook Question

In Exercises 23–34, find each product using either a horizontal or a vertical format. (xy+2)(x²y²−2xy+4)

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Textbook Question

In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (7x²y − 5xy) + (2x²y − xy)

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Textbook Question

In Exercises 33–68, add or subtract as indicated. (3x+2)/(3x+4) + (3x+6)/(3x+4)

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Textbook Question

In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (5x²y + 9xy + 12) + (−3x²y + 6xy + 3)

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (x+5)(x+8)

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Textbook Question

In Exercises 29–40, add the polynomials. Assume that all variable exponents represent whole numbers. (9x⁴y² − 6x²y² + 3xy) + (−18x⁴y² − 5x²y − xy)

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (y+5)(y−6)

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Textbook Question

Find each product. See Examples 3–5. (m-n+k)(m+2n-3k)

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Textbook Question

Find each product. See Examples 3–5. (r-3s+t)(2r-s+t)

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Textbook Question

Find each product. See Examples 3–5. (2x+3)(2x-3)(4x^2-9)

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (5x+3)(2x+1)

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Textbook Question

In Exercises 33–68, add or subtract as indicated. 5/x + 3

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Textbook Question

In Exercises 15–58, find each product. (x+5)^2

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Textbook Question

In Exercises 33–68, add or subtract as indicated. 3x/8 + x/12

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Textbook Question

Find each product. See Examples 5 and 6. (8s-3t)(8s+3t)

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (2x−3)(4x−5)

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Textbook Question

In Exercises 15–58, find each product. (x−3)^2

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Textbook Question

Find each product. See Examples 5 and 6. (4x^2-5y0(4x^2+5y)

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (x−3y)(2x+7y)

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Textbook Question

In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers. (x³ + 7xy − 5y²) − (6x³ − xy + 4y²)

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Textbook Question

Find each product. See Examples 5 and 6. (4m+2n)^2

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (7xy+1)(2xy−3)

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Textbook Question

In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers. (3x⁴y² + 5x³y − 3y) − (2x⁴y² − 3x³y − 4y + 6x)

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Textbook Question

In Exercises 33–68, add or subtract as indicated. 2/5x − (x+1)/4x

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Textbook Question

In Exercises 41–50, subtract the polynomials. Assume that all variable exponents represent whole numbers. (7y²ⁿ + yⁿ − 4) − (6y²ⁿ − yⁿ − 1)

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Textbook Question

In Exercises 33–68, add or subtract as indicated. (x+9)/10x^3 + 11/15x^2

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Textbook Question

Subtract −5a²b⁴ − 8ab² − ab from 3a²b⁴ − 5ab² + 7ab.

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Textbook Question

Find each product. See Examples 5 and 6. [(2p-3)+q]^2

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (7x³+5)(x²−2)

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Textbook Question

In Exercises 33–68, add or subtract as indicated. 3/(x+1) − 3/x

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Textbook Question

Find each product. See Examples 5 and 6. [(3q+5)-p][(3q+5)+p]

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Textbook Question

In Exercises 35–54, use the FOIL method to multiply the binomials. (3xⁿ−yⁿ)(xⁿ+2yⁿ)

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Textbook Question

Find each product. See Examples 5 and 6. [(9r-s)+2][(9r-s)-2]

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Textbook Question

In Exercises 55–68, multiply using one of the rules for the square of a binomial. (x + 3)²

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Textbook Question

In Exercises 33–68, add or subtract as indicated. 3x/(x−3) − (x+4)/(x+2)

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Textbook Question

In Exercises 55–68, multiply using one of the rules for the square of a binomial. (y − 5)²

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Textbook Question

In Exercises 15–58, find each product. (2x−3)^3

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Textbook Question

Find each product. See Examples 5 and 6. (z-3)^3

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Textbook Question

Find each product. See Examples 5 and 6. (q-2)^4

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Textbook Question

Find each product. See Examples 5 and 6. (r+3)^4

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Textbook Question

In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (7x^4 y^2−5x^2 y^2+3xy)+(−18x^4 y^2−6x^2 y^2−xy)

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Textbook Question

Perform the indicated operations. See Examples 2–6. -3(4q^2-3q+2) + 2(-q^2+q-4)

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Textbook Question

In Exercises 59–66, perform the indicated operations. Indicate the degree of the resulting polynomial. (3x^4 y^2+5x^3 y−3y)−(2x^4 y^2−3x^3 y−4y+6x)

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Textbook Question

In Exercises 55–68, multiply using one of the rules for the square of a binomial. (4xy² − xy)²

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Textbook Question

Perform the indicated operations. See Examples 2–6. 2(3r^2+4r+2) - 3(-r^2+4r-5)

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Textbook Question

In Exercises 55–68, multiply using one of the rules for the square of a binomial. (aⁿ + 4bⁿ)²

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Textbook Question

Perform the indicated operations. See Examples 2–6. m(5m-2) + 9(5-m)

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Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (x + 4)(x − 4)

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Textbook Question

In Exercises 67–82, find each product. (3x−y)(2x+5y)

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Textbook Question

In Exercises 67–82, find each product. (7x^2 y+1)(2x^2 y−3)

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Textbook Question

Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (-6x^3+7x^2-9x+3)+(14x^3+3x^2-11x-7)

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Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (4x + 7y)(4x − 7y)

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Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (8x + 7y)(8x − 7y)

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Textbook Question

In Exercises 67–82, find each product. (9x+7y)^2

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Textbook Question

Find each product : (3x-2)(4x^2+3x-5)

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Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (y³ + 2)(y³ − 2)

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Textbook Question

Find each product. Assume all variables represent positive real numbers. (x+x^1/2)(x-x^1/2)

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Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (y³ + 3)(y³ − 3)

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Textbook Question

In Exercises 67–82, find each product. (x−y)(x^2+xy+y^2)

252

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Textbook Question

Find each product. Assume all variables represent positive real numbers. (p^1/2-p^-1/2)(p^1/2+p^-1/2)

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Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (3xy² − 4y)(3xy² + 4y)

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Textbook Question

In Exercises 67–82, find each product. (7xy^2−10y)(7xy^2+10y)

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Textbook Question

In Exercises 69–82, multiply using the rule for the product of the sum and difference of two terms. (5aⁿ − 7)(5aⁿ + 7)

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Textbook Question

Find each product. (x+7y)(3x-5y)

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Textbook Question

In Exercises 83–94, find each product. (x + y + 3)(x + y − 3)

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Textbook Question

Find each product. (7x+4y)(7x-4y)

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Textbook Question

Find each product. (a-b)(a^+ab+b^2)

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Textbook Question

In Exercises 83–90, perform the indicated operations. Simplify the result, if possible. (y^−1−(y+2)^−1)/2

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Textbook Question

In Exercises 83–90, perform the indicated operation or operations. (2x−7)^5/(2x−7)^3

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Textbook Question

In Exercises 83–94, find each product. (x + 1)(x − 1)(x² + 1)

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Textbook Question

Exercises 108–110 will help you prepare for the material covered in the next section. Multiply: (2x³y²)(5x⁴y⁷).

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Textbook Question

Exercises 108–110 will help you prepare for the material covered in the next section. Simplify and express the polynomial in standard form: 3x(x² + 4x + 5) + 7(x² + 4x + 5)

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Textbook Question

The special products can be used to perform selected multiplications. On the left, we use (x+y)(x-y) = x^2-y^2. On the right, (x-y)^2 = x^2-2xy+y^2. Use special products to evaluate each expression. x = 63 y = 57

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Textbook Question

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. A number decreased by the sum of the number and four

In Exercises 121–128, write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Six times the product of negative five and a number

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Textbook Question

In Exercises 117–130, simplify each algebraic expression. 8(3x-5)-6x

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Textbook Question

In Exercises 117–130, simplify each algebraic expression. 5(3y-2)-(7y+2)

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Textbook Question

In Exercises 117–130, simplify each algebraic expression. 7-4[3-(4y-5)]

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Textbook Question

In Exercises 152–153, a polynomial is given in factored form. Use multiplication to find the product of the factors. (x + 4)(3x − 2y)

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Textbook Question

Simplify each complex fraction. [ (y+3)/y - 4/(y-1) ] / [ y/(y - 1) + 1/y ]

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Textbook Question

Simplify each complex fraction. [ (x+4)/x - 3/(x-2) ] / [ x/(x - 2) + 1/x ]

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0. Review of Algebra

Multiplying Polynomials

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