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.