Question

use the area model to multiply 2(7f + 10 + 12g). first, find the partial products. image of three rectangles labeled 7f, 10, 12g (top) and 2 (side) with boxes for partial products now, write the product. 2(7f + 10 + 12g) = blank submit

Explanation:

Step1: Multiply 2 by 7f

To find the partial product for the term with \( f \), we multiply 2 and \( 7f \). Using the distributive property of multiplication over addition, \( 2\times7f = 14f \).

Step2: Multiply 2 by 10

Next, we find the partial product for the constant term. Multiplying 2 and 10 gives \( 2\times10 = 20 \).

Step3: Multiply 2 by 12g

For the term with \( g \), we multiply 2 and \( 12g \). So, \( 2\times12g = 24g \).

Step4: Combine the partial products

Now, we add up all the partial products we found in the previous steps. So, \( 14f + 20 + 24g \). We can also rearrange the terms in standard form (usually alphabetical order of variables) as \( 14f + 24g + 20 \).

Answer:

\( 14f + 24g + 20 \)