What is expand ((10x^2+9)^3)/(3375) ?

The solution to expand ((10x^2+9)^3)/(3375) is (8x^6}{27}+(4x^4)/5+\frac{18x^2)/(25)+27/125

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expand ((10x^2+9)^3)/(3375)

expand

\frac{( 10 x ^{2} + 9 ) ^{3}}{3375}

\frac{8 x ^{6}}{27} + \frac{4 x ^{4}}{5} + \frac{18 x ^{2}}{25} + \frac{27}{125}

Solution steps

\frac{( 10 x ^{2} + 9 ) ^{3}}{3375}

(10 x^{2} + 9)^{3} = 1000 x^{6} + 2700 x^{4} + 2430 x^{2} + 729

= \frac{1000 x ^{6} + 2700 x ^{4} + 2430 x ^{2} + 729}{3375}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1000 x ^{6} + 2700 x ^{4} + 2430 x ^{2} + 729}{3375} = \frac{1000 x ^{6}}{3375} + \frac{2700 x ^{4}}{3375} + \frac{2430 x ^{2}}{3375} + \frac{729}{3375}

= \frac{1000 x ^{6}}{3375} + \frac{2700 x ^{4}}{3375} + \frac{2430 x ^{2}}{3375} + \frac{729}{3375}

\frac{1000 x ^{6}}{3375} = \frac{8 x ^{6}}{27}

\frac{2700 x ^{4}}{3375} = \frac{4 x ^{4}}{5}

\frac{2430 x ^{2}}{3375} = \frac{18 x ^{2}}{25}

\frac{729}{3375} = \frac{27}{125}

= \frac{8 x ^{6}}{27} + \frac{4 x ^{4}}{5} + \frac{18 x ^{2}}{25} + \frac{27}{125}

x (3 x - 2 = \frac{2}{5})

19600 (- 144 π + 3243)

\frac{4}{4 a ^{4}}

\frac{( 15 s + 49 ) s}{( s + 3 ) ( 5 s + 1 )}

cos^{2} (θ) - sin^{2} (θ)

What is expand ((10x^2+9)^3)/(3375) ?
The solution to expand ((10x^2+9)^3)/(3375) is (8x^6}{27}+(4x^4)/5+\frac{18x^2)/(25)+27/125