Question

use the area model to find the product (-3p + 2)(-p² + 3p + 5). first, find the partial products. now, write the product. (-3p + 2)(-p² + 3p + 5) =

Explanation:

Step1: Find partial products for -3p row

• Multiply -3p with \(-p^2\): \((-3p)(-p^2) = 3p^3\)
• Multiply -3p with \(3p\): \((-3p)(3p) = -9p^2\)
• Multiply -3p with \(5\): \((-3p)(5) = -15p\)

Step2: Find partial products for 2 row

• Multiply 2 with \(-p^2\): \(2(-p^2) = -2p^2\)
• Multiply 2 with \(3p\): \(2(3p) = 6p\)
• Multiply 2 with \(5\): \(2(5) = 10\)

Step3: Combine all partial products

Combine \(3p^3 - 9p^2 - 15p - 2p^2 + 6p + 10\). Combine like terms:

• For \(p^2\): \(-9p^2 - 2p^2 = -11p^2\)
• For \(p\): \(-15p + 6p = -9p\)

So the product is \(3p^3 - 11p^2 - 9p + 10\).

Answer:

Partial products (top row, left to right): \(3p^3\), \(-9p^2\), \(-15p\); (bottom row, left to right): \(-2p^2\), \(6p\), \(10\).
Product: \(3p^3 - 11p^2 - 9p + 10\)