Join the list of successful students who learned all the Factorization problems using the best material provided on our website. Yes, it’s true. Students can easily score good marks in the exam using our information on Factoring Differences of Squares. Also, we are giving all Factorization-Related Solved Problems, Extra Questions, and also Multiple Choice Questions and Answers. Utilize this opportunity and start your practice now and test your knowledge on the concept.
Factoring the Differences of Two Squares Examples
1. Factorize the following algebraic expressions
(i) 64 – a2
Solution:
Given expression is 64 – a2
Rewrite the above expression.
82 – a2
The above equation 82 – a2 is in the form of a2 – b2.
[(8)2 – (a)2]
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 8 and b = a
(8 + a) (8 – a)
The final answer is (8 + a) (8 – a)
(ii) 3m2 – 27n2
Solution:
Given expression is 3m2 – 27n2
Rewrite the above expression. Take 3 common.
3 (m2 – (3n)2) where 9n2 = (3n)2
The above equation (m2 – (3n)2) is in the form of a2 – b2.
[(m)2 – (3n)2]
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = m and b = 3n
(m + 3n) (m – 3n)
3{(m + 3n) (m – 3n)}
The final answer is 3{(m + 3n) (m – 3n)}
(iii) a3 – 25a
Solution:
Given expression is a3 – 25a
Rewrite the above expression. Take a common.
a (a2 – 25)
a ((a)2 – (5)2)
The above equation ((a)2 – (5)2) is in the form of a2 – b2.
((a)2 – (5)2)
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = a and b = 5
(a + 5) (a – 5)
a {(a + 5) (a – 5)}
The final answer is a {(a + 5) (a – 5)}
2. Factor the expressions
(i) 81x2 – (y – z)2
Solution:
Given expression is 81x2 – (y – z)2
Rewrite the above expression.
(9x)2 – (y – z)2
The above equation ((9x)2 – (y – z)2) is in the form of a2 – b2.
((9x)2 – (y – z)2)
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 9x and b = y – z
(9x + (y – z)) (9x – (y – z))
(9x + y – z) (9x – y + z)
The final answer is (9x + y – z) (9x – y + z)
(ii) 25(a + b)2 – 36(a – 2b)2.
Solution:
Given expression is 25(a + b)2 – 36(a – 2b)2
Rewrite the above expression.
{5(a + b)}2 – {6(a – 2b)}2
The above equation {5(a + b)}2 – {6(a – 2b)}2 is in the form of a2 – b2.
((5(a + b))2 – (6(a – 2b))2)
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = 5(a + b) and b = 6(a – 2b)
[5(a + b) + 6(a – 2b)] [5(a + b) – 6(a – 2b)]
[5a + 5b + 6a – 12b] [5a + 5b – 6a + 12b]
[11a – 7b] [17b – a]
The final answer is [11a – 7b] [17b – a]
(iii) (m – 2)2 – (m – 3)2
Solution:
Given expression is (m – 2)2 – (m – 3)2
The above equation (m – 2)2 – (m – 3)2 is in the form of a2 – b2.
(m – 2)2 – (m – 3)2
Now, apply the formula of a2 – b2 = (a + b) (a – b), where a = m – 2 and b = m – 3
[(m – 2) + (m – 3)] [(m – 2) – (m – 3)]
[m – 2 + m – 3] [m – 2 – m + 3]
[2m – 5] [1]
[2m – 5]
The final answer is [2m – 5]
