Question

use the area model to find the product $3a(-4a^2 + a - 5)$. first, find the partial products. $-4a^2$ $a$ $-5$ $3a$ now, write the product. $3a(-4a^2 + a - 5) = \square$

Explanation:

Step1: Find first partial product

Multiply \(3a\) and \(-4a^2\): \(3a\times(-4a^2)= -12a^{3}\)

Step2: Find second partial product

Multiply \(3a\) and \(a\): \(3a\times a = 3a^{2}\)

Step3: Find third partial product

Multiply \(3a\) and \(-5\): \(3a\times(-5)= -15a\)

Step4: Combine partial products

Add the partial products: \(-12a^{3}+3a^{2}-15a\)

Answer:

\(-12a^{3} + 3a^{2} - 15a\)