Factorization of Expressions of the Form a^3 + b^3 | How to Factorize Expressions in the Form a^3 + b^3?

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Learn how to factorize Expressions of the Form a3 + b3 by referring to the entire article. Here we will use the concept of algebraic identity to factor the given expressions. Factorizing is the process of writing an expression into a product of two expressions which results in the given expression.

Know how to factorize the expressions in the form or can be put in the form a3 + b3 with the step-by-step explanations provided. Check out the Problems on Factorization of Expressions of the form a3 + b3 and learn the problem-solving approach used.

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Problems on Factorization of Expressions a^3 + b^3

Example 1.
Factorize x3 + 64y3?
Solution:
Given Expression = x3 + 64y3
=(x)3+(4y)3
=(x+4y){(x)2 – (x)(4y) + (4y)2}
=(x+4y)(x2-4xy+16y2)

Example 2.
Factorize a6 + b6?
Solution:
Given Expression = a6 + b6
=(a2)3 + (b2)3
= (a2 + b2){(a2)2 – a2 ∙ b2 + (b2)2}
= (a2 + b2)(a4 – a2b2 + b4)

Example 3.
Factorize 1 + 216z3?
Solution:
Given Expression = 1 + 216z3
=13 + (6z)3
= (1 + 6z{12 – 1 ∙ 6z + (6z)2 }
=(1 + 6z)(1 – 6z +36z2)

Example 4.
Factorize 27x3 + 1/x3?
Solution:
Given Expression = 27x3 + 1/x3
=(3x)3+(1/x)3
=(3x+1/x)((3x)2-3x.1/x+(1/x)2)
=(3x+1/x)(9x2-3+1/x2)

Example 5.
Factorize a6 + 1?
Solution:
Given Expression = a6 + 1
=(a2)3+(1)3
=(a2+1)((a2)2-a2.1+(1)2)
=(a2+1)(a4-a2.1+1)

Example 6.
Factorize the Expression 125u3 + 64v3?
Solution:
Given Expression = 125u3 + 64v3
= (5u)3+(4v)3
=(5u+4v)((5u)2-5u.4v+(4v)2)
=(5u+4v)(25u2-20uv+16v2)

 

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