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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)?

1. Go through the given binomial expression.
2. Now relate the formula to the given expression.
3. Apply the suitable formula and substitute the values in it.
4. 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