|
English
|
Difference of CubesDescription 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  |