dylan uses the expressions $(x^{2}-2x + 8)$ and $(2x^{2}+5x - 7)$ to represent the length and width of his…

dylan uses the expressions $(x^{2}-2x + 8)$ and $(2x^{2}+5x - 7)$ to represent the length and width of his bedroom. which expression represents the area ($lw$) of dylans room?\n$2x^{4}-10x^{2}-56$\n$2x^{4}+10x^{2}+56$\n$2x^{4}+x^{3}-x^{2}+54x - 56$\n$2x^{4}+9x^{3}+33x^{2}+54x + 56$

dylan uses the expressions $(x^{2}-2x + 8)$ and $(2x^{2}+5x - 7)$ to represent the length and width of his bedroom. which expression represents the area ($lw$) of dylans room?\n$2x^{4}-10x^{2}-56$\n$2x^{4}+10x^{2}+56$\n$2x^{4}+x^{3}-x^{2}+54x - 56$\n$2x^{4}+9x^{3}+33x^{2}+54x + 56$

Answer

Explanation:

Step1: Recall area formula

The area of a rectangle is $A = l\times w$, where $l$ is length and $w$ is width. Here, $l=x^{2}-2x + 8$ and $w=2x^{2}+5x - 7$. So $A=(x^{2}-2x + 8)(2x^{2}+5x - 7)$.

Step2: Use distributive property

[ \begin{align*} A&=x^{2}(2x^{2}+5x - 7)-2x(2x^{2}+5x - 7)+8(2x^{2}+5x - 7)\ &=(2x^{4}+5x^{3}-7x^{2})-(4x^{3}+10x^{2}-14x)+(16x^{2}+40x - 56) \end{align*} ]

Step3: Remove parentheses and combine like - terms

[ \begin{align*} A&=2x^{4}+5x^{3}-7x^{2}-4x^{3}-10x^{2}+14x + 16x^{2}+40x - 56\ &=2x^{4}+(5x^{3}-4x^{3})+(-7x^{2}-10x^{2}+16x^{2})+(14x + 40x)-56\ &=2x^{4}+x^{3}-x^{2}+54x - 56 \end{align*} ]

Answer:

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