Question

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

Answer 1

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

$2x^4 + x^3 - x^2 +54x - 56$

Answer 2

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