Question

the perimeter of a rectangle is represented by $4x^{2}+6x - 2$. the perimeter of a smaller rectangle is represented by $x^{2}+4x + 5$. which polynomial expression best represents how much larger the first rectangle is than the smaller rectangle? a $3x^{2}+2x - 7$ b $3x^{2}+2x - 3$ c $3x^{2}+10x + 3$ d $5x^{2}+10x - 7$ e $5x^{2}-8x - 7$

Explanation:

Step1: Set up the subtraction

To find how much larger the first rectangle is than the smaller one, we subtract the perimeter of the smaller rectangle from the perimeter of the larger rectangle. So we have $(4x^{2}+6x - 2)-(x^{2}+3x + 5)$.

Step2: Distribute the negative sign

$4x^{2}+6x - 2 - x^{2}-3x - 5$.

Step3: Combine like - terms

$(4x^{2}-x^{2})+(6x - 3x)+(-2 - 5)=3x^{2}+3x - 7$.

Answer:

A. $3x^{2}+3x - 7$