a^2-b^2 Formula

The a² - b² formula is also known as "the difference of squares formula".

• It is one of the algebraic identities.
• It is used to factorize the binomials of squares.

What is a^2-b^2 Formula?

The a² - b² formula is:

a² - b² = (a - b) (a + b)

If you would like to verify this, you can just multiply (a - b) (a + b) and see whether you get a² - b². 

You can understand this formula geometrically using the following figure:

Solved Examples Using a^2-b^2 Formula

Example 1: 

Find the value of 106² - 6².

Solution: To find: 100² - 6².

Let us assume that a = 100 and b = 6.

We will substitute these in the a² - b² formula.

a² - b² = (a - b) (a + b)

106² - 6² = (106 - 6) (106 + 6)

= (100) (112)

= 11200

Answer: 106² - 6² = 11200.

Example 2: 

Factorize the expression 25x² - 64.

Solution: To factorize: 25x² - 64.

We will use the a² - b² formula to factorize this.

We can write the given expression as

25x² - 64 = (5x)² - 8²

We will substitute a = 5x and b = 8 in the formula of a² - b². 

a² - b² = (a - b) (a + b)

(5x)² - 8² = (5x - 8) (5x + 8)

Answer: 25x² - 64 = (5x - 8) (5x + 8)