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 a^{3} – b^{3}. 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 a ^{3} – b^{3} = (a – b)(a^{2} + ab + b^{2})**

See More: Factorization of Expressions of the Form a^3 + b^3

## Factorization of Expressions of the form a^{3} – b^{3}

**Example 1.**

Factorize 8x^{3} – 27?

**Solution:
**Given Expression = 8x

^{3}– 27

We can write the expression as (2x)

^{3}-(3)

^{3}

= (2x – 3){(2x)

^{2}+ 2x ∙ 3 + 3

^{2}}

=(2x-3)(4x

^{2}+6x+9)

**Example 2.
**Factorize the Expression 1-64y

^{3}?

**Solution:**

Given Expression = 1-64y

^{3}

We can write the given expression as (1)

^{3}-(4y)

^{3}

=(1-4y)(1

^{2}+1.4y+(4y)

^{2})

=(1-4y)(1=4y+16y

^{2})

**Example 3.
**Factorize the Expression 216x

^{6}– y

^{6}?

**Solution:**

Given Expression = (6x

^{2})

^{3}– (y

^{2})

^{3}

= ( 6x

^{2}– y

^{2}){(6x

^{2})

^{2}+ 4x

^{2}∙ y

^{2}+ (y

^{2})

^{2}}

= ( 6x

^{2}– y

^{2})(36x

^{4}+ 4x

^{2}y

^{2}+ y

^{4})

= (6x + y)(6x – y)(36x

^{4}+ 4x

^{2}y

^{2}+ y

^{4})

**Example 4.
**Factorize 343x

^{3}– 1/x

^{3}

**Solution:**

Given Expression = 343x

^{3}– 1/x

^{3}

=(7x)

^{3}-(1/x)

^{3}

=(7x-1/x)((7x)

^{2}+7x.1/x+(1/x)

^{2})

=(7x-1/x)(49x

^{2}-7+1/x

^{2})

**Example 5.
**Factorize the Expression 512u

^{3}– 64v

^{3}

**Solution:**

Given Expression = 512u

^{3}– 64v

^{3}

= (8u)

^{3}– (4v)

^{3}

=(8u-4v)((8u)

^{2}+8u.4v+(4v)

^{2})

=(8u-4v)(64u

^{2}+32uv+16v

^{2})

**Example 6.
**Factorize the Expression y

^{6}– z

^{6}

**Solution:**

Given Expression = y

^{6}– z

^{6}

=(y

^{2})

^{3}– (z

^{2})

^{3}

= (y

^{2}– z

^{2}){(y

^{2})

^{2}+ y

^{2}∙ z

^{2}+ (z

^{2})

^{2}}

= (y

^{2}– z

^{2})(y

^{4}+ y

^{2}∙ z

^{2}+ z

^{4})