How do you factor and simplify ${sin}^{3} x + 27$ $sin^3x+27$ ?

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Answer 1 · 2016-09-20T11:25:02

${sin}^{3} x + 27 = (sin x + 3) ({sin}^{2} - 3 sin x + 9)$ $sin^3x+27=(sinx+3)(sin^2-3sinx+9)$

${sin}^{3} x + 27$ $sin^3x+27$

= $({(sin x)}^{3} + 3^{3})$ $((sinx)^3+3^3)$

Now using identity $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ $a^3+b^3=(a+b)(a^2-ab+b^2)$

this is $(sin x + 3) ({sin}^{2} - 3 sin x + 9)$ $(sinx+3)(sin^2-3sinx+9)$

How do you factor and simplify sin3x+27sin^3x+27?