Question

which polynomial represents the area of the rectangle? 2x + 5 x - 2 2x^{2}-x - 10 2x^{2}+x - 10 2x^{2}-9x - 10 2x^{2}-10

Explanation:

Step1: Recall area formula

The area formula for a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width. Here, $l=2x + 5$ and $w=x - 2$.

Step2: Expand the product

$(2x + 5)(x - 2)=2x\times x+2x\times(- 2)+5\times x + 5\times(-2)$.

Step3: Simplify the terms

$2x\times x=2x^{2}$, $2x\times(-2)=-4x$, $5\times x = 5x$, $5\times(-2)=-10$. Then $2x^{2}-4x + 5x-10$.

Step4: Combine like - terms

$-4x+5x=x$, so the area is $2x^{2}+x - 10$.

Answer:

$2x^{2}+x - 10$