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English
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Sum of CubesDescription The Sum 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 Sum 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  |