Question

use the area model to find the product $(-8b + 3)(-8b - 3)$. first, find the partial products. now, write the product. simplify your answer. $(-8b + 3)(-8b - 3) = $

Explanation:

Step1: Find the partial products

To find the partial products using the area model (which is like the distributive property or FOIL for binomials), we multiply each term in the first binomial by each term in the second binomial.

• Multiply \(-8b\) (from the first binomial) by \(-8b\) (from the second binomial): \((-8b) \times (-8b) = 64b^2\)
• Multiply \(-8b\) (from the first binomial) by \(-3\) (from the second binomial): \((-8b) \times (-3) = 24b\)
• Multiply \(3\) (from the first binomial) by \(-8b\) (from the second binomial): \(3 \times (-8b) = -24b\)
• Multiply \(3\) (from the first binomial) by \(-3\) (from the second binomial): \(3 \times (-3) = -9\)

Step2: Combine the partial products

Now, we add up all the partial products: \(64b^2 + 24b - 24b - 9\)

The \(24b\) and \(-24b\) terms cancel each other out (since \(24b - 24b = 0\)), so we are left with \(64b^2 - 9\)

Answer:

\(64b^2 - 9\)