Sum of Cubes

Reference > Algebra: Sums and Differences of Squares and Cubes

Description

The Sum 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 Sum 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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