# Difference of Two Squares | Factoring Difference of Two Squares

Before you start practicing the Difference of Two Squares Concept know the step-by-step process to solve the Factoring Difference of Two Squares. Therefore, students can easily learn all types of factoring problems here. Without any late, begin your practice and finish solving every problem included. Refer to Solved Examples on Difference of Two Squares with Answers Provided.

## Difference of Two Squares Questions

1. m4 – (n + r)4

Solution:
Given expression is m4 – (n + r)4
Rewrite the given expression in the form of a2 – b2.
(m2)2 – ( (n + r)2)2
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = m2 and b = (n + r)2
[m2 + (n + r)2] [m2 – (n + r)2]
[m2 + n2 + r2 + 2nr] [(m)2 – (n + r)2]
From the above equation, [(m)2 – (n + r)2] is in the form of a2 – b2.
[(m)2 – (n + r)2]
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = m and b = (n + r)
[m + (n + r)] [m – (n + r)]
Now, [m2 + n2 + r2 + 2nr] [(m)2 – (n + r)2]
[m2 + n2 + r2 + 2nr] [m + (n + r)] [m – (n + r)]
[m2 + n2 + r2 + 2nr] [m + n + r] [m – n – r]

The final answer is [m2 + n2 + r2 + 2nr] [m + n + r] [m – n – r]

2. 4a2 – b2 + 6b – 9.

Solution:
Given expression is 4a2 – b2 + 6b – 9.
Rewrite the given expression.
4a2 – (b2 – 6b + 9)
b2 – 6b + 9 is in the form of a2 – b2 + 2ab where a = b, b = 3
We know that a2 – b2 + 2ab = (a – b)2
Therefore, b2 – 6b + 9 = (b – 3)2
So, 4a2 – (b – 3)2
The above equation 4a2 – (b – 3)2 is in the form of a2 – b2.
[(2a)2 – (b – 3)2]
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 2a and b = (b – 3)
(2a + b – 3) {2a – (b – 3)},
(2a + b – 3) (2a – b – 3)

The final answer is (2a + b – 3) (2a – b – 3)

3. 25x2 – (4m2 – 12mn + 9n2)

Solution:
Given expression is 25x2 – (4m2 – 12mn + 9n2)
(4m2 – 12mn + 9n2) is in the form of a2 – b2 + 2ab where a = 2m, b = 3n
We know that a2 – b2 + 2ab = (a – b)2
Therefore, (4m2 – 12mn + 9n2) = (2m – 3n)2
So, 25x2 – (2m – 3n)2
The above equation 25x2 – (2m – 3n)2 is in the form of a2 – b2.
[(5x)2 – (2m – 3n)2]
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 5x and b = (2m – 3n)
[5x + (2m – 3n)] [5x – (2m – 3n)]
(5x + 2m – 3n) (5x – 2m + 3n)

The final answer is (5x + 2m – 3n) (5x – 2m + 3n)

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