Use the area model to write the simplified expression for the total area below.
A) $x ^ { 2 } + 3 x$
B) $x ^ { 2 } + 9$
C) $x ^ { 2 } + 9 x$
D) $x ^ { 2 } + 6 x + 9$
E) $x ^ { 2 } + 3 x + 9$

Question

Use the area model to write the simplified expression for the total area below. 
A) $x ^ { 2 } + 3 x$ 
B) $x ^ { 2 } + 9$ 
C) $x ^ { 2 } + 9 x$ 
D) $x ^ { 2 } + 6 x + 9$ 
E) $x ^ { 2 } + 3 x + 9$

Quizplus · Accepted Answer

The area model shows that the total area is the sum of the areas of the two squares (with side lengths x and 3) and the rectangle (with length x and width 3). The area of the first square is x^2, the area of the second square is 3^2=9, and the area of the rectangle is 3x. Therefore, the total area is x^2 + 9 + 3x, which simplifies to choice D: x^2 + 6x + 9.

Use the Area Model to Write the Simplified Expression for the Total