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Question Number 22061 by NECx last updated on 10/Oct/17

$$\mathrm{If}{9\mathrm{x}}^2+6\mathrm{xy}+{4\mathrm{y}}^2\mathrm{is}\mathrm{a}\mathrm{factor}\mathrm{of}$$$${27\mathrm{x}}^3-{8\mathrm{y}}^3.\mathrm{find}\mathrm{the}\mathrm{other}\mathrm{factor}.$$

Answered by sma3l2996 last updated on 10/Oct/17

$$27x^3-8y^3={\left(3x\right)}^3-{\left(2y\right)}^3=(3x-2y)({\left(3x\right)}^2+3x\times 2y+{\left(2y\right)}^2)$$$$=(3x-2y)(9x^2+6xy+4y^2)$$$$sotheotherfactoris3x-2y$$

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