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

The solution to expand (3y^2(-3y+3)^2)/2 is (27y^4)/2-27y^3+(27y^2)/2

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

expand

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

\frac{27 y ^{4}}{2} - 27 y^{3} + \frac{27 y ^{2}}{2}

Solution steps

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

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

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

Expand

3 y^{2} (9 y^{2} - 18 y + 9) : 27 y^{4} - 54 y^{3} + 27 y^{2}

= \frac{27 y ^{4} - 54 y ^{3} + 27 y ^{2}}{2}

Apply the fraction rule:

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

\frac{27 y ^{4} - 54 y ^{3} + 27 y ^{2}}{2} = \frac{27 y ^{4}}{2} - \frac{54 y ^{3}}{2} + \frac{27 y ^{2}}{2}

= \frac{27 y ^{4}}{2} - \frac{54 y ^{3}}{2} + \frac{27 y ^{2}}{2}

Divide the numbers:

\frac{54}{2} = 27

= \frac{27 y ^{4}}{2} - 27 y^{3} + \frac{27 y ^{2}}{2}

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\frac{x + 7}{( x + 1 ) ^{2}}

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What is expand (3y^2(-3y+3)^2)/2 ?
The solution to expand (3y^2(-3y+3)^2)/2 is (27y^4)/2-27y^3+(27y^2)/2