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

The solution to expand (3x(-2x-y+3)^2)/2 is 6x^2y+6x^3-18x^2+(3xy^2)/2-9xy+(27x)/2

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

expand

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

6 x^{2} y + 6 x^{3} - 18 x^{2} + \frac{3 x y ^{2}}{2} - 9 x y + \frac{27 x}{2}

Solution steps

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

(- 2 x - y + 3)^{2} = 4 x y + 4 x^{2} - 12 x + y^{2} - 6 y + 9

= \frac{3 x ( 4 x ^{2} + 4 x y - 12 x + y ^{2} + 9 - 6 y )}{2}

Expand

3 x (4 x y + 4 x^{2} - 12 x + y^{2} - 6 y + 9) : 12 x^{2} y + 12 x^{3} - 36 x^{2} + 3 x y^{2} - 18 x y + 27 x

= \frac{12 x ^{2} y + 12 x ^{3} - 36 x ^{2} + 3 x y ^{2} - 18 x y + 27 x}{2}

Apply the fraction rule:

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

\frac{12 x ^{2} y + 12 x ^{3} - 36 x ^{2} + 3 x y ^{2} - 18 x y + 27 x}{2} = \frac{12 x ^{2} y}{2} + \frac{12 x ^{3}}{2} - \frac{36 x ^{2}}{2} + \frac{3 x y ^{2}}{2} - \frac{18 x y}{2} + \frac{27 x}{2}

= \frac{12 x ^{2} y}{2} + \frac{12 x ^{3}}{2} - \frac{36 x ^{2}}{2} + \frac{3 x y ^{2}}{2} - \frac{18 x y}{2} + \frac{27 x}{2}

\frac{12 x ^{2} y}{2} = 6 x^{2} y

\frac{12 x ^{3}}{2} = 6 x^{3}

\frac{36 x ^{2}}{2} = 18 x^{2}

\frac{18 x y}{2} = 9 x y

= 6 x^{2} y + 6 x^{3} - 18 x^{2} + \frac{3 x y ^{2}}{2} - 9 x y + \frac{27 x}{2}

\frac{2 ( 60 x ^{4} - 53 x ^{2} + 12 )}{x ( 3 x ^{2} + 4 ) ( 20 x ^{2} + 3 )}

(1 + e^{2 x}) (- 2 e^{2 x})

(- 1, 9) p a sses t h ro ug h (- 20, - 7)

\frac{3 ( s - 1 )}{s ^{2} + 13 s + 36}

sinh (l) e f t (x y + z^{2})

What is expand (3x(-2x-y+3)^2)/2 ?
The solution to expand (3x(-2x-y+3)^2)/2 is 6x^2y+6x^3-18x^2+(3xy^2)/2-9xy+(27x)/2