Question

Each side of a square x units long is decreased by 9 units. Which expression represents the area of the new square in square units? *

Answer 1

Given:

Side of a square = x units

The side of square is decreased by 9 units.

To find:

The expression that represents the area of the new square in square units.

Solution:

It is given that, the side of a square is x units and it is decreased by 9 units. So, the side of new square is:

$\text{New side length}=x-9$

The area of a square is:

$Area=(side)^2$

So, the area of the new square is:

$Area=(x-9)^2$

$Area=(x)^2-2(x)(9)+(9)^2$          $[\because (a-b)^2=a^2-2ab+b^2]$

$Area=x^2-18x+81$

Therefore, the expression for the area of the new square is either $(x-9)^2$ or $x^2-18x+81$, both are equivalent.