5. Which polynomial, written in simplified form, represents the area of this rectangle?
A. $8 x^{2}-36 x y-20 y^{2}$
B. $8 x^{2}+22 x y-20 y^{2}$
C. $16 x^{2}+72 x y-40 y^{2}$
D. $8 x^{2}+36 x y-20 y^{2}$

Answer

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Answer

\boxed{D. 8x^2 + 36xy - 20y^2}

Steps

Step 1 ：Analyze each polynomial and see if it can be factored into two expressions representing the length and width of the rectangle.

Step 2 ：Factoring each polynomial: $A = 4(x - 5y)(2x + y)$, $B = 2(4x^2 + 11xy - 10y^2)$, $C = 8(x + 5y)(2x - y)$, $D = 4(x + 5y)(2x - y)$

Step 3 ：\boxed{D. 8x^2 + 36xy - 20y^2}