Question

a square painting has an area of 81x^2-90x-25. A second square painting has an area of 25x^2+30x+9. What is an expression that represent the difference of the area of the paintings? show two ways to find the solution

Answer 1

Answer:

The answer in the procedure

Step-by-step explanation:

Let

A1 ------> the area of the first square painting

A2 ---->  the area of the second square painting

D -----> the difference of the areas

we have

$A1=81x^{2}-90x-25$

$A2=25x^{2}+30x+9$

case 1) The area of the second square painting is greater than the area of the first square painting

The difference of the area of the paintings is equal to subtract the area of the first square painting from the area of the second square painting

D=A2-A1

$D=(25x^{2}+30x+9)-(81x^{2}-90x-25)$

$D=(-56x^{2}+120x+34)$

case 2) The area of the first square painting is greater than the area of the second square painting

The difference of the area of the paintings is equal to subtract the area of the second square painting from the area of the first square painting

D=A1-A2

$D=(81x^{2}-90x-25)-(25x^{2}+30x+9)$

$D=(56x^{2}-120x-34)$