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

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

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

Muzahedul Raton · Accepted Answer

Final Answer : D, Explanation :  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.

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Use the area model to write the simplified expression for the total area below. A) x2+3xx ^ { 2 } + 3 xx2+3x B) x2+9x ^ { 2 } + 9x2+9 C) x2+9xx ^ { 2 } + 9 xx2+9x D) x2+6x+9x ^ { 2 } + 6 x + 9x2+6x+9 E) x2+3x+9x ^ { 2 } + 3 x + 9x2+3x+9

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