Add or subtract, as indicated. See Example 4. 2(12y² - 8y + 6) - 4(3y² - 4y +2)

Verified step by step guidance

1. Distribute the 2 into the first polynomial: $2(12y^2-8y+6)=2\times 12y^2-2\times 8y+2\times 6$.
2. Simplify the expression from the first distribution: $24y^2-16y+12$.
3. Distribute the -4 into the second polynomial: $-4(3y^2-4y+2)=-4\times 3y^2+4\times 4y-4\times 2$.
4. Simplify the expression from the second distribution: $-12y^2+16y-8$.
5. Combine like terms from the two simplified expressions: $(24y^2-16y+12)+(-12y^2+16y-8)$.

Key Concepts

Distributive Property

The distributive property states that a(b + c) = ab + ac. This principle allows us to multiply a single term by each term within a parenthesis. In the context of the given expression, applying the distributive property is essential for expanding the terms correctly before combining like terms.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This process simplifies expressions and is crucial for obtaining a final simplified form. In the provided question, after distributing, you will need to identify and combine the coefficients of the like terms.

Polynomial Expressions

A polynomial expression is a mathematical expression that consists of variables raised to whole number exponents and their coefficients. Understanding how to manipulate polynomials, including addition, subtraction, and distribution, is fundamental in algebra. The expression in the question is a polynomial, and recognizing its structure is key to solving the problem.