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## Simplification of (a + b)(a – b)

(a + b)(a – b) = a(a – b) + b(a – b)

(a + b)(a – b) = a² – ab + ab – b²

(a + b)(a – b) = a² – b²

### How to Simplify (a + b)(a – b)?

- Go through the given binomial expression.
- Now relate the formula to the given expression.
- Apply the suitable formula and substitute the values in it.
- Finally, simplify the values.

Also, Refer:

### Solved Examples on Simplification of (a + b)(a – b)

**Example 1.**

Simply the equation (m – 1/m + 3) (m – 1/m -3)

**Solution:**

Given that

(m – 1/m + 3) (m – 1/m -3)

This is in the form of (a + b) ( a – b)

We know that

(a + b) ( a – b) = a² + b²

Here

m – 1/m = a ; 3 = b

Substitute a, b in the above equation

(m – 1/m + 3) (m – 1/m -3) = (m – 1/m)² + 3²

m² – 1/m² + 9

Therefore the solution is m² – 1/m² + 9

**Example 2.**

Simply the equation (6x + 2) (6x – 2)

**Solution:**

Given that

(6x + 2) (6x – 2)

This is in the form of (a + b) ( a – b)

We know that

(a + b) ( a – b) = a² + b²

Here

a = 6x ; b = 2

Substitute a,b in the above equation

(6x + 2) (6x – 2) = (6x)² + 2²

36x² + 4

Therefore the solution is 36x² + 4

**Example 3.**

Simply the equation (2n + 6) ( 2n – 6)

**Solution:**

Given that

(2n + 6) (2n – 6)

This is in the form of (a + b) ( a – b)

We know that

(a + b) ( a – b) = a² + b²

Here

a = 2n ; b = 6

Substitute a, b in the above equation

(2n + 6) (2n – 6) = (2n)² + 6²

4n² + 36

Therefore the solution is 4n² + 36

**Example 4.**

Simply the equation (8/2 m + 1) ( 8/2 m – 1)

**Solution:**

Given that

(8/2 m + 1) ( 8/2 m – 1)

This is in the form of (a + b) ( a – b)

We know that

(a + b) ( a – b) = a² + b²

Here

a = 8/2 m ; b = 1

Substitute a, b in the above equation

(8/2 m + 1) (8/2 m – 1) = (8/2 m)² + 1²

16m² + 1

Therefore the solution is 16m² + 1

**Example 5.**

Simply the equation (24x + 6) ( 24x – 6)

**Solution:**

Given that

(24x + 6) (24x – 6)

This is in the form of (a + b) ( a – b)

We know that

(a + b) ( a – b) = a² + b²

Here

a = 2n ; b = 6

Substitute a, b in the above equation

(24x + 6) (24x – 6) = (24x)² + 6²

576x² + 36

Therefore the solution is 576x² + 36