In this article of ours, you will find various problems on finding the factorization using a2 – b2. Learn how to approach when you are given an algebraic expression using the basic identity a2 – b2 = (a+b)(a-b). Solve the problems available here and learn different models of questions framed on the topic. Master the concept and learn factor algebraic expressions much easily by employing these simple identities. Try to answer the questions on your own and then cross-check with our solutions.

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## Questions on Factorizing using a2 – b2 Identity

Example 1.
Factorize: 16a2 – b2 + 4a + b
Solution:
Given expression = 16a2 – b2 + 4a + b
= (16a2 – b2) + 4a + b
= {(4a)2 – b2} + 4a + b
= (4a + b)(4a – b) + 1(4a + b)
= (4a + b)(4a – b + 1)

Example 2.
Factorize: x3 – 5x2 – x + 5
Solution:
Given expression = x3 – 5x2 – x + 5
= (x3 – 5x2) – x + 5
= x2(x – 5) – 1(x – 5)
= (x – 5)(x2 – 1)
= (x – 5)(x2 – 12)
= (x – 5)(x + 1)(x – 1)

Example 3.
Factorize: 5x2 – y2+ 2x – 2y – 4xy
Solution:
Given expression = 5x2 – y2+ 2x – 2y – 4xy
= x2 – y2 + 2x – 2y + 4x2 – 4xy
= (x + y)(x – y) + 2(x – y) + 4x(x – y)
= (x – y)(x + y + 2 + 4x)
= (x – y)(5x + y + 2)

Example 4.
Factorize: a4+ a2b2 + b4
Solution:
Given expression = a4 +a2b2 + b4
= a4+2a2b2 -a2b2+ b4
= (a2)2 + 2 ∙ a2 ∙ b2 + (b2)2 – a2b2
= (a2 + b2)2 – (ab)2
= (a2 + b2 + ab)( a2 + b2 – ab)

Example 5.
Factorize x2 + xy – 4y – 16
Solution:
Given Expression = x2 + xy – 4y – 16
= (x2 – 16) + xy – 4y
= (x2 – 42) + y(x – 4)
= (x + 4)(x – 4) + y(x – 4)
= (x – 4)(x +4 + y)
= (x – 4)(x + y + 4)

Example 6.
Factorize x(x – 6) – y(y – 6)
Solution:
Given Expression = x(x – 6) – y(y – 6)
=x2-6x-y2+6y
= (x2 – y2) – 6x + 6y
= x2 – 6x – y2 + 6y
= (x + y)(x – y) – 6(x – y)
= (x – y)(x + y – 6)

Example 7.
Factorize a4  + 49?
Solution:
Given Expression = a4  + 49
=(a2)2 + 72
= (a2)2 + 2 ∙ a2 ∙ 7 + 72 – 2 ∙ a2 ∙ 7
= (a2 + 7)2 – 14a2
= (a2 + 7)2 – (√14a)2
= (a2+ 7 + √14a)(a2 + 7 – √14a)
=(a2+ 7 + √14a)(a2 + 7 – √14a)

Example 8.
Express x2 – 5x + 6?
Solution:
Given Expression = x2 – 5x + 6
= x2 -3x-2x+6
= x(x-3)-2(x-3)
=(x-2)(x-3)