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. < SEE SAMPLE B> 71^2

Verified step by step guidance

1. Recognize that 71^2 can be expressed as (70+1)^2.
2. Use the special product formula for a binomial square: (a+b)^2 = a^2 + 2ab + b^2.
3. Identify a = 70 and b = 1 in the expression (70+1)^2.
4. Substitute a and b into the formula: (70+1)^2 = 70^2 + 2(70)(1) + 1^2.
5. Calculate each term separately: 70^2, 2(70)(1), and 1^2, then sum them to find the result.

Key Concepts

Special Products

Special products refer to specific algebraic identities that simplify the multiplication of binomials. Common examples include the difference of squares, (a+b)(a-b) = a^2 - b^2, and the square of a binomial, (a+b)^2 = a^2 + 2ab + b^2. These identities allow for quicker calculations and a deeper understanding of polynomial behavior.

Difference of Squares

The difference of squares is a specific case of special products where the expression takes the form (a+b)(a-b). This identity states that the product equals the square of the first term minus the square of the second term, expressed as a^2 - b^2. It is particularly useful for factoring and simplifying expressions involving squares.

Square of a Binomial

The square of a binomial is another special product that expands the expression (a+b)^2 into a^2 + 2ab + b^2. This formula is essential for simplifying expressions and solving equations involving squared terms. Understanding this concept helps in evaluating expressions like 71^2 by recognizing it as (70+1)^2.