What is expand (L(3L+3uL)^2)/(60) ?

The solution to expand (L(3L+3uL)^2)/(60) is (3L^3u^2)/(20)+(3L^3u)/(10)+(3L^3)/(20)

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expand (L(3L+3uL)^2)/(60)

expand

\frac{L ( 3 L + 3 uL ) ^{2}}{60}

\frac{3 L ^{3} u ^{2}}{20} + \frac{3 L ^{3} u}{10} + \frac{3 L ^{3}}{20}

Solution steps

\frac{L ( 3 L + 3 uL ) ^{2}}{60}

(3 L + 3 uL)^{2} = 9 L^{2} + 18 L^{2} u + 9 L^{2} u^{2}

= \frac{L ( 9 L ^{2} u ^{2} + 18 L ^{2} u + 9 L ^{2} )}{60}

Factor

L (9 L^{2} + 18 L^{2} u + 9 L^{2} u^{2}) : 9 L^{3} (1 + 2 u + u^{2})

= \frac{9 L ^{3} ( 1 + 2 u + u ^{2} )}{60}

Cancel the common factor:

3

= \frac{3 L ^{3} ( u ^{2} + 2 u + 1 )}{20}

Expand

3 L^{3} (u^{2} + 2 u + 1) : 3 L^{3} u^{2} + 6 L^{3} u + 3 L^{3}

= \frac{3 L ^{3} u ^{2} + 6 L ^{3} u + 3 L ^{3}}{20}

Apply the fraction rule:

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

\frac{3 L ^{3} u ^{2} + 6 L ^{3} u + 3 L ^{3}}{20} = \frac{3 L ^{3} u ^{2}}{20} + \frac{6 L ^{3} u}{20} + \frac{3 L ^{3}}{20}

= \frac{3 L ^{3} u ^{2}}{20} + \frac{6 L ^{3} u}{20} + \frac{3 L ^{3}}{20}

Cancel

\frac{6 L ^{3} u}{20} : \frac{3 L ^{3} u}{10}

= \frac{3 L ^{3} u ^{2}}{20} + \frac{3 L ^{3} u}{10} + \frac{3 L ^{3}}{20}

x (cos (x) - sin (x))

(((3 x^{2} + 2 x + 1) \cdot cos (3 x))^{'})^{2021}

16

sin (x) \cdot (1 - sin (x))

\frac{x ^{2} - 4}{x - 2}

What is expand (L(3L+3uL)^2)/(60) ?
The solution to expand (L(3L+3uL)^2)/(60) is (3L^3u^2)/(20)+(3L^3u)/(10)+(3L^3)/(20)