Difference of Cubes

Reference > Algebra: Sums and Differences of Squares and Cubes

Description

The Difference of Cubes Rule states that:

a3−b3=(a−b)(a2+ab+b2){a}^{3}-{b}^{3}=(a-b)({a}^{2}+ab+{b}^{2})
Examples
8x3−27{8x}^{3}-27
1
Rewrite it in the form a3−b3{a}^{3}-{b}^{3}, where a=2xa=2x and b=3b=3.
(2x)3−33{(2x)}^{3}-{3}^{3}

2
Use Difference of Cubes: a3−b3=(a−b)(a2+ab+b2){a}^{3}-{b}^{3}=(a-b)({a}^{2}+ab+{b}^{2}).
(2x−3)((2x)2+(2x)(3)+32)(2x-3)({(2x)}^{2}+(2x)(3)+{3}^{2})

3
Use Multiplication Distributive Property: (xy)a=xaya{(xy)}^{a}={x}^{a}{y}^{a}.
(2x−3)(22x2+2x×3+32)(2x-3)({2}^{2}{x}^{2}+2x\times 3+{3}^{2})

4
Simplify  22{2}^{2}  to  44.
(2x−3)(4x2+2x×3+32)(2x-3)(4{x}^{2}+2x\times 3+{3}^{2})

5
Simplify  32{3}^{2}  to  99.
(2x−3)(4x2+2x×3+9)(2x-3)(4{x}^{2}+2x\times 3+9)

6
Simplify  2x×32x\times 3  to  6x6x.
(2x−3)(4x2+6x+9)(2x-3)(4{x}^{2}+6x+9)

Done

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