Find each product. (3w+2)(-w2+4w-3)

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 36

Chapter 1, Problem 36

Find each product. (3w+2)(-w²+4w-3)

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Identify the two binomials to be multiplied: $(3w + 2)$ and $(-w^2 + 4w - 3)$.

Apply the distributive property (also known as the FOIL method for binomials) by multiplying each term in the first polynomial by each term in the second polynomial.

Multiply \$3w$ by each term in $(-w^2 + 4w - 3)$ to get: $3w \times (-w^2)$, $3w \times 4w$, and $3w \times (-3)$.

Multiply $2$ by each term in $(-w^2 + 4w - 3)$ to get: $2 \times (-w^2)$, $2 \times 4w$, and $2 \times (-3)$.

Combine all the products from the previous steps and then simplify by combining like terms to write the final expanded expression.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Polynomial Multiplication

Polynomial multiplication involves multiplying each term in one polynomial by every term in the other polynomial. This process requires distributing terms carefully to ensure all products are accounted for, combining like terms afterward to simplify the expression.

Distributive Property

The distributive property states that a(b + c) = ab + ac. It is essential for multiplying polynomials because it allows you to multiply each term inside one polynomial by each term in the other, ensuring no terms are missed during expansion.

Combining Like Terms

After multiplying polynomials, you often get several terms with the same variable raised to the same power. Combining like terms means adding or subtracting their coefficients to simplify the expression into a standard polynomial form.