If you want to learn the process of Factorization of Expressions of the Form a^3 – b^3 then this page is going to be extremely helpful as it covers how to factorize the difference of cubes. Refer to the further modules to know about the problem-solving approach when given an expression of the form a3 – b3. We have given step-by-step solutions for all the factorization example questions provided so that you can clearly understand the topic as well as resolve any doubts about the topic if any.
Formula for a3 – b3 = (a – b)(a2 + ab + b2)
See More: Factorization of Expressions of the Form a^3 + b^3
Factorization of Expressions of the form a3 – b3
Example 1.
Factorize 8x3 – 27?
Solution:
Given Expression = 8x3 – 27
We can write the expression as (2x)3-(3)3
= (2x – 3){(2x)2 + 2x ∙ 3 + 32}
=(2x-3)(4x2+6x+9)
Example 2.
Factorize the Expression 1-64y3?
Solution:
Given Expression = 1-64y3
We can write the given expression as (1)3-(4y)3
=(1-4y)(12+1.4y+(4y)2)
=(1-4y)(1=4y+16y2)
Example 3.
Factorize the Expression 216x6 – y6?
Solution:
Given Expression = (6x2)3 – (y2)3
= ( 6x2– y2){(6x2)2 + 4x2 ∙ y2 + (y2)2}
= ( 6x2– y2)(36x4 + 4x2y2 + y4)
= (6x + y)(6x – y)(36x4 + 4x2y2 + y4)
Example 4.
Factorize 343x3 – 1/x3
Solution:
Given Expression = 343x3 – 1/x3
=(7x)3-(1/x)3
=(7x-1/x)((7x)2+7x.1/x+(1/x)2)
=(7x-1/x)(49x2-7+1/x2)
Example 5.
Factorize the Expression 512u3 – 64v3
Solution:
Given Expression = 512u3 – 64v3
= (8u)3– (4v)3
=(8u-4v)((8u)2+8u.4v+(4v)2)
=(8u-4v)(64u2+32uv+16v2)
Example 6.
Factorize the Expression y6 – z6
Solution:
Given Expression = y6 – z6
=(y2)3 – (z2)3
= (y2 – z2){(y2)2 + y2 ∙ z 2 + (z2)2}
= (y2 – z2)(y4 + y2 ∙ z 2 + z4)