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:
[tex]\text{New side length}=x-9[/tex]
The area of a square is:
[tex]Area=(side)^2[/tex]
So, the area of the new square is:
[tex]Area=(x-9)^2[/tex]
[tex]Area=(x)^2-2(x)(9)+(9)^2[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex]Area=x^2-18x+81[/tex]
Therefore, the expression for the area of the new square is either [tex](x-9)^2[/tex] or [tex]x^2-18x+81[/tex], both are equivalent.
