Cube of Difference

Reference > Algebra: Sums And Differences Of Squares And Cubes

Description

The Cube of Difference Rule states that:

\({(a-b)}^{3}={a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}\)
Examples
\[{x}^{3}-6{x}^{2}+12x-8\]
1
Rewrite it in the form \({a}^{3}-3{a}^{2}b+3a{b}^{2}-{b}^{3}\), where \(a=x\) and \(b=2\)
\[{x}^{3}-3{x}^{2}(2)+3(x)\times {2}^{2}-{2}^{3}\]

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

Done