Factoring a polynomial is the product of the two or more polynomials. Learn How to Factorize the Difference of Two Squares in this article. Break down all the huge algebraic expressions into small factors with the help of factorization. Solved Problems on Factoring the Difference of Two Squares are explained clearly along with the solutions. Visit all factorization problems and get complete knowledge of the factorization concept.
Solved Problems on How to Factorize the Difference of Two Squares
1. Factorize the following algebraic expressions
(i) m2 – 121
Solution:
Given expression is m2 – 121
Rewrite the above expression.
m2 – (11)2
The above equation m2 – (11)2 is in the form of a2 – b2.
m2 – (11)2
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = m and b = 11
(m + 11) (m – 11)
The final answer is (m + 11) (m – 11)
(ii) 49a2 – 16b2
Solution:
Given expression is 49a2 – 16b2
Rewrite the above expression.
(7a)2 – (4b)2
The above equation (7a)2 – (4b)2 is in the form of a2 – b2.
(7a)2 – (4b)2
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 7a and b = 4b
(7a + 4b) (7a – 4b)
The final answer is (7a + 4b) (7a – 4b)
2. Factor the following
(i) 48m2 – 243n2
Solution:
Given expression is 48m2 – 243n2
Take 3 common
3{16m2 – 81n2}
Rewrite the above expression.
3{(4m)2 – (9n)2}
The above equation {(4m)2 – (9n)2} is in the form of a2 – b2.
{(4m)2 – (9n)2}
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 4m and b = 9n
(4m + 9n) (4m – 9n)
3{(4m + 9n) (4m – 9n)}
The final answer is 3{(4m + 9n) (4m – 9n)}
(ii) 3a3 – 48a
Solution:
Given expression is 3a3 – 48a
Take 3 common
3a{a2 – 16}
Rewrite the above expression.
3a{(a)2 – (4)2}
The above equation {(a)2 – (4)2} is in the form of a2 – b2.
{(a)2 – (4)2}
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = a and b = 4
(a + 4) (a – 4)
3a{(a + 4) (a – 4)}
The final answer is 3a{(a + 4) (a – 4)}
3. Factor the expressions
(i) 25(a + 3b)2 – 16 (a – 3b)2
Solution:
Given expression is 25(a + 3b)2 – 16 (a – 3b)2
Rewrite the above expression.
{[5(a + 3b)]2 – [4 (a – 3b)]2}
The above equation {[5(a + 3b)]2 – [4 (a – 3b)]2} is in the form of a2 – b2.
{[5(a + 3b)]2 – [4 (a – 3b)]2}
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 5(a + 3b) and b = 4 (a – 3b)
(5(a + 3b) + 4 (a – 3b)) (5(a + 3b) – [4 (a – 3b)])
(5a + 15b + 4a – 12b) (5a + 15b – 4a + 12b)
(9a + 3b) (a + 27b)
3(3a + b) (a + 27b)
The final answer is 3(3a + b) (a + 27b)
(ii) 4x2 – 16/(25x2)
Solution:
Given expression is 4x2 – 16/(25x2)
Rewrite the above expression.
{[2x]2 – [4/5x]2}
The above equation {[2x]2 – [4/5x]2} is in the form of a2 – b2.
{[2x]2 – [4/5x]2}
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 2x and b = 4/5x
(2x + 4/5x) (2x – 4/5x)
The final answer is (2x + 4/5x) (2x – 4/5x)