What is expand (3(-2x^2+24x))/((5x^2-2x+12)^2) ?

The solution to expand (3(-2x^2+24x))/((5x^2-2x+12)^2) is (-6x^2+72x)/(25x^4-20x^3+124x^2-48x+144)

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expand (3(-2x^2+24x))/((5x^2-2x+12)^2)

expand

\frac{3 ( - 2 x ^{2} + 24 x )}{( 5 x ^{2} - 2 x + 12 ) ^{2}}

\frac{- 6 x ^{2} + 72 x}{25 x ^{4} - 20 x ^{3} + 124 x ^{2} - 48 x + 144}

Solution steps

\frac{3 ( - 2 x ^{2} + 24 x )}{( 5 x ^{2} - 2 x + 12 ) ^{2}}

(5 x^{2} - 2 x + 12)^{2} = 25 x^{4} - 20 x^{3} + 124 x^{2} - 48 x + 144

= \frac{3 ( - 2 x ^{2} + 24 x )}{25 x ^{4} - 20 x ^{3} + 124 x ^{2} - 48 x + 144}

Expand

3 (- 2 x^{2} + 24 x) : - 6 x^{2} + 72 x

= \frac{- 6 x ^{2} + 72 x}{25 x ^{4} - 20 x ^{3} + 124 x ^{2} - 48 x + 144}

(t - \frac{1}{4}) (t - \frac{1}{2})

(x^{1} + x^{2} = 2,) (x^{1} + x^{2} = - 15)

(a x + 36 + 6 + 2 x) (a x + 36 - 6 - 2 x)

(x - \frac{7}{3})^{2}

What is expand (3(-2x^2+24x))/((5x^2-2x+12)^2) ?
The solution to expand (3(-2x^2+24x))/((5x^2-2x+12)^2) is (-6x^2+72x)/(25x^4-20x^3+124x^2-48x+144)