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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