What is expand (5(3x^3+2x)^{3/2}(9x^2+2))/2 ?

The solution to expand (5(3x^3+2x)^{3/2}(9x^2+2))/2 is (45x^2(3x^3+2x)^{3/2})/2+5(3x^3+2x)^{3/2}

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expand (5(3x^3+2x)^{3/2}(9x^2+2))/2

expand

\frac{5 ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}} ( 9 x ^{2} + 2 )}{2}

\frac{45 x ^{2} ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}}}{2} + 5 (3 x^{3} + 2 x)^{\frac{3}{2}}

Solution steps

\frac{5 ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}} ( 9 x ^{2} + 2 )}{2}

Expand

5 (3 x^{3} + 2 x)^{\frac{3}{2}} (9 x^{2} + 2) : 45 x^{2} (3 x^{3} + 2 x)^{\frac{3}{2}} + 10 (3 x^{3} + 2 x)^{\frac{3}{2}}

= \frac{45 x ^{2} ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}} + 10 ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}}}{2}

Apply the fraction rule:

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

\frac{45 x ^{2} ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}} + 10 ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}}}{2} = \frac{45 x ^{2} ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}}}{2} + \frac{10 ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}}}{2}

= \frac{45 x ^{2} ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}}}{2} + \frac{10 ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}}}{2}

Divide the numbers:

\frac{10}{2} = 5

= \frac{45 x ^{2} ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}}}{2} + 5 (3 x^{3} + 2 x)^{\frac{3}{2}}

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What is expand (5(3x^3+2x)^{3/2}(9x^2+2))/2 ?
The solution to expand (5(3x^3+2x)^{3/2}(9x^2+2))/2 is (45x^2(3x^3+2x)^{3/2})/2+5(3x^3+2x)^{3/2}