Question

What is the product of the polynomials below?

(8x-4x-8)(2 +3x+2)
A. 16x* +16x°-12x? -16x-6
B. 16x+16x -12x? -16x -16
C. 16x +16x-12x²-32x-16
D. 16x* +16x-12x? -32x -6

Answer 1

To find the product of the given polynomials, distribute each term of the first polynomial across the terms of the second polynomial, combine like terms, and simplify. The correct product is 16x² + 12x² - 32x -16.

Step-by-step explanation:

The product of the polynomials (8x - 4x - 8) and (2 + 3x + 2) can be found by applying the distributive property, also known as the FOIL method in the following manner:

1. Multiply the first terms: 8x × 2 = 16x².
2. Multiply the outer terms: 8x × 3x = 24x².
3. Multiply the inner terms: -4x × 2 = -8x.
4. Multiply the last terms: -4x × 3x = -12x².
5. Multiply the first terms with the last term: -8 × 2 = -16.
6. Multiply the last terms of both binomials: -8 × 3x = -24x.
7. Multiply the last term of the first polynomial with the middle term of the second: -8 × 2 = -16.

Now, combine like terms:

16x² + 24x² - 12x² - 8x - 24x - 16

Simplify terms:

16x² + 12x² - 32x - 16

The correct product of the polynomials is therefore: 16x² + 12x² - 32x -16, which corresponds to option C.