How to simplify Difference of Two Squares

A difference of two square is an expression where we have to subtract a squared number from another squared number.

An example is 5² - 2²

When this happens, we say we have a difference of two square expression.

Although the expression 5² - 2² appears simple as we can easily simplify it as follows:

Example1

Simplify 5² - 2²

Solution

5² - 2²

= 5*5 – 2*2

= 25 – 4

= 21

But where more complicated expressions are involved, we will not be able to use the approach above. In this case, we resort to the use of difference of two square formula stated below

X² – y² = (x+y)(x-y)

This is the formula that is used for difference of two square expressions.

Example1 above can be simplified using this formula as follows

5² - 2²

= (5+2)(5-3)

= 7 * 3

= 21 (as above)

Example2

Simplify 87² – 53² using difference of two square approach

Solution

87² – 53²

= (87+53)(87-53)

= 140 * 34

= 4760

Example3

Simplify (x+1)² – x²

Solution

(x+1)² – x²

= (x+1)² – x²

= [(x+1)+(x)][(x+1) – (x)]

= (x+1+x)( x+1-x)

= (x+x+1)(x-x+1)

= (2x+1)(1)

= 1*(2x+1)

= 2x+1