Learn how to factorize Expressions of the Form a^{3} + b^{3} 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 a^{3} + b^{3} with the step-by-step explanations provided. Check out the Problems on Factorization of Expressions of the form a^{3} + b^{3} and learn the problem-solving approach used.

Also, Check:

- Problems on Factorization of Expressions of the Form x^2 +(a + b)x +ab
- Factorization of Expressions of the Form x^2 + (a + b)x + ab

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

**Example 1.
**Factorize x

^{3}+ 64y

^{3}?

**Solution:**

Given Expression = x

^{3}+ 64y

^{3}

=(x)

^{3}+(4y)

^{3}

=(x+4y){(x)

^{2}– (x)(4y) + (4y)

^{2}}

=(x+4y)(x

^{2}-4xy+16y

^{2})

**Example 2.
**Factorize a

^{6}+ b

^{6}?

**Solution:**

Given Expression = a

^{6}+ b

^{6}

=(a

^{2})

^{3}+ (b

^{2})

^{3}

= (a

^{2}+ b

^{2}){(a

^{2})

^{2}– a

^{2}∙ b

^{2}+ (b

^{2})

^{2}}

= (a

^{2}+ b

^{2})(a

^{4}– a

^{2}b

^{2}+ b

^{4})

**Example 3.
**Factorize 1 + 216z

^{3}?

**Solution:**

Given Expression = 1 + 216z

^{3}

=1

^{3}+ (6z)

^{3}

= (1 + 6z{1

^{2}– 1 ∙ 6z + (6z)

^{2}}

=(1 + 6z)(1 – 6z +36z

^{2})

**Example 4.
**Factorize 27x

^{3}+ 1/x

^{3}?

**Solution:**

Given Expression = 27x

^{3}+ 1/x

^{3}

=(3x)

^{3}+(1/x)

^{3}

=(3x+1/x)((3x)

^{2}-3x.1/x+(1/x)

^{2})

=(3x+1/x)(9x

^{2}-3+1/x

^{2})

**Example 5.
**Factorize a

^{6}+ 1?

**Solution:**

Given Expression = a

^{6}+ 1

=(a

^{2})

^{3}+(1)

^{3}

=(a

^{2}+1)((a

^{2})

^{2}-a

^{2}.1+(1)

^{2})

=(a

^{2}+1)(a

^{4}-a

^{2}.1+1)

**Example 6.
**Factorize the Expression 125u

^{3}+ 64v

^{3}?

**Solution:**

Given Expression = 125u

^{3}+ 64v

^{3}

= (5u)

^{3}+(4v)

^{3}

=(5u+4v)((5u)

^{2}-5u.4v+(4v)

^{2})

=(5u+4v)(25u

^{2}-20uv+16v

^{2})