Difference of Cubes

Reference > Algebra: Sums And Differences Of Squares And Cubes

Description

The Difference of Cubes Rule states that:

\({a}^{3}-{b}^{3}=(a-b)({a}^{2}+ab+{b}^{2})\)
Examples
\[{8x}^{3}-27\]
1
Rewrite it in the form \({a}^{3}-{b}^{3}\), where \(a=2x\) and \(b=3\)
\[{(2x)}^{3}-{3}^{3}\]

2
Use Difference of Cubes: \({a}^{3}-{b}^{3}=(a-b)({a}^{2}+ab+{b}^{2})\)
\[(2x-3)({(2x)}^{2}+(2x)(3)+{3}^{2})\]

3
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\)
\[(2x-3)({2}^{2}{x}^{2}+2x\times 3+{3}^{2})\]

4
Simplify \({2}^{2}\) to \(4\)
\[(2x-3)(4{x}^{2}+2x\times 3+{3}^{2})\]

5
Simplify \({3}^{2}\) to \(9\)
\[(2x-3)(4{x}^{2}+2x\times 3+9)\]

6
Simplify \(2x\times 3\) to \(6x\)
\[(2x-3)(4{x}^{2}+6x+9)\]

Done