What is expand (3y(-3y+3)^2)/2 ?

The solution to expand (3y(-3y+3)^2)/2 is (27y^3)/2-27y^2+(27y)/2

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expand (3y(-3y+3)^2)/2

expand

\frac{3 y ( - 3 y + 3 ) ^{2}}{2}

\frac{27 y ^{3}}{2} - 27 y^{2} + \frac{27 y}{2}

Solution steps

\frac{3 y ( - 3 y + 3 ) ^{2}}{2}

(- 3 y + 3)^{2} = 9 y^{2} - 18 y + 9

= \frac{3 y ( 9 y ^{2} - 18 y + 9 )}{2}

Expand

3 y (9 y^{2} - 18 y + 9) : 27 y^{3} - 54 y^{2} + 27 y

= \frac{27 y ^{3} - 54 y ^{2} + 27 y}{2}

Apply the fraction rule:

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

\frac{27 y ^{3} - 54 y ^{2} + 27 y}{2} = \frac{27 y ^{3}}{2} - \frac{54 y ^{2}}{2} + \frac{27 y}{2}

= \frac{27 y ^{3}}{2} - \frac{54 y ^{2}}{2} + \frac{27 y}{2}

Divide the numbers:

\frac{54}{2} = 27

= \frac{27 y ^{3}}{2} - 27 y^{2} + \frac{27 y}{2}

\frac{a ^{2} + b}{a ( b + c )}

(x)^{\frac{1}{3}}

\frac{x}{( x + 1 ) ( x + 2 ) ( x + 3 )}

\frac{s + 5}{( s ^{2} + 10 s + 29 ) ^{2}}

\frac{1}{s ( s + 1 ) ( s ^{2} + 4 s + 13 )}

What is expand (3y(-3y+3)^2)/2 ?
The solution to expand (3y(-3y+3)^2)/2 is (27y^3)/2-27y^2+(27y)/2