There are different topics and formulas in Expansion of Powers of Binomials and Trinomials. We can simplify all the problems by using different formulas. This article helps you to select the right formula and solve the given questions in the Worksheet on Simplification of (a + b)(a – b). We can simplify the given binomial expression by using the brackets. Click on the solution to find the step-by-step explanations for all the questions.
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Simplification of (a + b)(a – b) Worksheet
Check out the given problems and learn the simple methods to find the solution.
Example 1.
Simply the equation (n – 1/n + 5) (n – 1/n – 5)
Solution:
Given that
(n – 1/n + 5) (n – 1/n – 5)
This is in the form of (a + b) ( a – b)
We know that
(a + b) ( a – b) = a² – b²
Here
n – 1/n = a ; 5 = b
(n – 1/n + 5) (n – 1/n – 5) = (n – 1/n)² – 5²
n² – 1/n² – 25
Thus the simplification of (n – 1/n + 5) (n – 1/n – 5) is n² – 1/n² – 25
Example 2.
Simply the equation (12x + 6) (12x – 6)
Solution:
Given that
(12x + 6) (12x – 6)
This is in the form of (a + b) ( a – b)
We know that
(a + b) ( a – b) = a² – b²
Here
a = 12x ; b = 6
Substitute a, b in the above equation
(12x + 6) (12x – 6) = (12x)² – 6²
144x² – 36
Therefore the solution is 144x² – 36
Example 3.
Simply the equation (6x + 1) (6x – 1)
Solution:
Given that
(6x + 1) (6x – 1)
This is in the form of (a + b) ( a – b)
We know that
(a + b) ( a – b) = a² – b²
Here
a = 6x ; b = 1
Substitute a, b in the above equation
(6x + 2) (6x – 2) = (6x)² – 1²
36x² – 1
Therefore the solution is 36x² – 1
Example 4.
Simply the equation (1/2x + 11) (1/2x – 11)
Solution:
Given that
(1/2x + 11) (1/2x -11)
This is in the form of (a + b) ( a – b)
We know that
(a + b) ( a – b) = a² – b²
Here
a = 1/2x ; b = 11
Substitute a, b in the above equation
(1/2x + 2) (1/2x – 2) = (1/2x)² – 11²
1/4x² – 121
Therefore the solution is 1/4x² – 121
Example 5.
Simply the equation (x + 22) (x – 22)
Solution:
Given that,
(x + 22) (x – 22)
This is in the form of (a + b) ( a – b)
We know that
(a + b) ( a – b) = a² – b²
Here
a = x ; b = 22
Substitute a, b in the above equation
(x + 22) (x – 22) = (x)² – 22²
x² – 484
Therefore the solution is x² – 484
Example 6.
Simply the equation (2p/q + 7) (2p/q – 7)
Solution:
Given that
(2p/q + 7) (2p/q – 7)
This is in the form of (a + b) ( a – b)
We know that
(a + b) ( a – b) = a² – b²
Here
a = 2p/q ; b = 7
Substitute a, b in the above equation
(2p/q + 7) (2p/q – 7) = (2p/q)² – 7²
4p/q² – 49
Therefore the solution is 4p/q² – 49
Example 7.
Simply the equation (x + 13) (x – 13)
Solution:
Given that
(x + 13) (x – 13)
This is in the form of (a + b) ( a – b)
We know that
(a + b) ( a – b) = a² – b²
Here
a = x ; b = 13
Substitute a, b in the above equation
(x + 13) (x – 13) = (x)² – 13²
x² – 169
Therefore the solution is x²+ 169
Example 8.
Simply the equation (2n + 36) ( 2n – 36)
Solution:
Given that
(2n + 36) (2n – 36)
This is in the form of (a + b) ( a – b)
We know that
(a + b) ( a – b) = a² + b²
Here
a = 2n ; b = 36
Substitute a, b in the above equation
(2n + 36) (2n – 36) = (2n)² + 36²
4n² + 1296
Therefore the solution is 4n² + 1296
Example 9.
Simply the equation (2/3n + 6) ( 2/3n – 6)
Solution:
Given that
(2/3n + 6) (2/3n – 6)
This is in the form of (a + b) ( a – b)
We know that
(a + b) ( a – b) = a² + b²
Here
a = 2/3n ; b = 6
Substitute a, b in the above equation
(2/3n + 6) (2/3n – 6) = (2/3n)² + 6²
4/6n² + 36
Therefore the solution is 4/6n² + 36
Example 10.
Simply the equation (n + 26) ( n – 26)
Solution:
Given that
(n + 26) (n – 26)
This is in the form of (a + b) ( a – b)
We know that
(a + b) ( a – b) = a² + b²
Here
a = n ; b = 26
Substitute a, b in the above equation
(n + 26) (n – 26) = (n)² + 26²
n² + 676
Therefore the solution is n² + 676