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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?
A. 2x^4-10x-56
B. 2x^4+10x+56
C. 2x^4+x^3-x^2+54x-56
D. 2x^4+9x^3+33x^2+54x+56

Respuesta :

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 : [tex]C.2x^4+x^3-x^2+54x-56 [/tex]

Length of his  room =[tex] (x^2 - 2x + 8)[/tex]

Width of his room  = [tex](2x^2 + 5x - 7) [/tex]

We know the formula for Area

Area = Length * Width

Area = [tex](x^2 - 2x + 8)(2x^2 + 5x - 7)[/tex]

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

So it becomes,

[tex]2x^4 + 5x^3 - 7x^2 -4x^3 -10x^2 +14x +16x^2 +40x - 56 [/tex]

Now combine like terms

[tex]2x^4 + x^3 - x^2 +54x - 56 [/tex]

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