Question

use the area model to find the product $(3p^2 + 2)(3p^2 + 2)$. first, find the partial products. now, write the product. simplify your answer. $(3p^2 + 2)(3p^2 + 2) = \boxed{}$

Explanation:

Step1: Find partial products

• Yellow cell: \(3p^2 \times 3p^2 = 9p^4\)
• Cyan cell: \(3p^2 \times 2 = 6p^2\)
• Orange cell: \(2 \times 3p^2 = 6p^2\)
• Pink cell: \(2 \times 2 = 4\)

Step2: Sum partial products

Add all partial products: \(9p^4 + 6p^2 + 6p^2 + 4\)
Simplify like terms: \(9p^4 + 12p^2 + 4\)

Answer:

\(9p^4 + 12p^2 + 4\)