Question

use the area model to find the product (3v + 7)(3v + 7). first, find the partial products. 3v 7 3v 7 now, write the product. simplify your answer. (3v + 7)(3v + 7) =

Explanation:

Step1: Find partial products

• Yellow cell: Multiply \(3v\) and \(3v\), so \(3v\times3v = 9v^2\).
• Teal cell: Multiply \(3v\) and \(7\), so \(3v\times7 = 21v\).
• Orange cell: Multiply \(7\) and \(3v\), so \(7\times3v = 21v\).
• Pink cell: Multiply \(7\) and \(7\), so \(7\times7 = 49\).

Step2: Sum partial products

Add the four partial products: \(9v^2 + 21v + 21v + 49\). Combine like terms (\(21v + 21v = 42v\)) to get \(9v^2 + 42v + 49\).

Answer:

\(9v^2 + 42v + 49\)