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Dylan uses the expressions (x2 – 2x + 8) and (2x2 + 5x – 7) to represent the length and width of his bedroom. Which expression represents the area (lw) of Dylan’s room?

A2x^4-10x-56
B2x^4+10x+56
C2x^4+x^3-x^2+54x-56
D2x^4+9x^3+33x^2+54x+56

Verified Answer :

texaschic101

u find the area by multiplying length and width to arrive at the answer, which is : C. 2x^4 + x^3 - x^2 + 54x - 56

Answer : \(C.2x^4+x^3-x^2+54x-56\)

Length of his  room =\((x^2 - 2x + 8)\)

Width of his room  = \((2x^2 + 5x - 7)\)

We know the formula for Area

Area = Length * Width

Area = \((x^2 - 2x + 8)(2x^2 + 5x - 7)\)

We multiply each term inside first parenthesis with each term inside the second parenthesis.

So it becomes,

\(2x^4 + 5x^3 - 7x^2 -4x^3 -10x^2 +14x +16x^2 +40x - 56\)

Now combine like terms

\(2x^4 + x^3 - x^2 +54x - 56\)

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