Factorizing Algebraic Expressions is a way of changing the sum of terms into products of smaller ones. Factorizing using Identities makes the process of finding factors of algebraic expressions much simple. Here we have covered various problems on factorization of expressions of the form a2-b2. In this article, you will find several Factorization of Algebraic Expressions using Identity Examples explained clearly step by step. Use them as a quick guide if you are stuck with any problem and clear your doubts in no time.
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Factorization of Expressions using Identity a2-b2 with Examples
Example 1.
Resolve the expression 64a2 – 81b2 into factors?
Solution:
Given Expression is 64a2 – 81b2
We can rewrite them as (8a)2– (9b)2
As per the identity a2-b2 =(a+b)(a-b), thus (8a)2– (9b)2 can be written as (8a+9b)(8a-9b)
Therefore, (8a)2– (9b)2 resolved into factors is (8a+9b)(8a-9b)
Example 2.
Factorize (x + y)2 – 9(x – y)2
Solution:
Given (x + y)2 – 9(x – y)2
= {(x + y)2 – (3(x – y))2}
= {(x+y+3(x-y)}{x+y-3(x-y)}
Therefore, (x + y)2 – 9(x – y)2 resolved into factors is {(x+y+3(x-y)}{x+y-3(x-y)}
Example 3.
Factorize the expression (x2 + y2 – z2)2 – 16x2y2 of the form a2 – b2?
Solution:
Given (x2 + y2 – z2)2 – 16x2y2
= (x2 + y2 – z2)2 – (4xy)2
= (x2 + y2 – z2+4xy)(x2 + y2 – z2-4xy)
Example 4.
Factorize 4x2-64?
Solution:
Given 4x2-64
Rewriting it we have
= 4(x2-16)
=4(x-4)(x+4)
Therefore, 4x2-64 factorized is 4(x-4)(x+4)
Example 5.
Factorize 64(a+b)2-(a-b)2
Solution:
Given 64(a+b)2-(a-b)2
= {8(a+b)}2-(a-b)2}
= {8(a + b) + (a – b)}{8(a + b) – (a – b)}
= (8a + 8b + a – b)(8a + 8b – a + b)
= (9a + 7b)(7a + 9b)
Example 6.
Factorize 1- (c-d)2
Solution:
Given Expression 1- (c-d)2
= (1)2-(c-d)2
=(1+(c-d))(1-(c-d))
Example 7.
Factorize 25a4 – 16b4
Solution:
Given 25a4 – 16b4
= (5a2)2-(4b2)2
=(5a2+4b2)(5a2-4b2)
Example 8.
Factorize a4 – 81b4
Solution:
Given a4 – 81b4
=(a2)2-(9b2)2
=(a2+9b2)(a2-9b2)