Question

Suppose you cut a small square from a square of fabric as shown in the diagram. Write an expression for the remaining shaded area. Factor the expression. Type your answer below.

Answer 1

The area of the larger square is x^2
The area of the small square is 3*3 = 9
To find the area of the shaded region you subtract the two values.
x^2 - 9

The factored form of this is (x + 3)(x - 3)

Answer 2

`(x+3)(x-3)`

Explanation:

we know that

The remaining shaded area is equal to the area of the complete square minus the area of the small square

so

The area of complete square is equal to

`A1=x^(2)\ units^(2)`

The area of the small square is equal to

`A2=3^(2)=9\ units^(2)`

The area of the remaining shaded area is equal to

`A1-A2=(x^(2) -9)\ units^(2)`

`(x^(2) -9)\ units^(2)=(x+3)(x-3))\ units^(2)`