Question

1. (7r² - 6r - 6)(2r - 4)

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply each term in the first polynomial by each term in the second polynomial:
$$(7r^2)(2r) + (7r^2)(-4) + (-6r)(2r) + (-6r)(-4) + (-6)(2r) + (-6)(-4)$$

Step2: Simplify each product

Calculate each term:
$$14r^3 - 28r^2 - 12r^2 + 24r - 12r + 24$$

Step3: Combine like terms

Combine the \(r^2\) terms and the \(r\) terms:

• For \(r^2\): \(-28r^2 - 12r^2 = -40r^2\)
• For \(r\): \(24r - 12r = 12r\)

So the simplified polynomial is:
$$14r^3 - 40r^2 + 12r + 24$$

Answer:

\(14r^3 - 40r^2 + 12r + 24\)