What is expand 6/((9-4x)^{-2)} ?

The solution to expand 6/((9-4x)^{-2)} is 96x^2-432x+486

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expand 6/((9-4x)^{-2)}

expand

\frac{6}{( 9 - 4 x ) ^{- 2}}

96 x^{2} - 432 x + 486

Solution steps

\frac{6}{( 9 - 4 x ) ^{- 2}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(9 - 4 x)^{- 2} = \frac{1}{( 9 - 4 x ) ^{2}}

= \frac{6}{\frac{1}{( 9 - 4 x ) ^{2}}}

Apply the fraction rule:

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

= \frac{6 ( 9 - 4 x ) ^{2}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 6 (9 - 4 x)^{2}

(9 - 4 x)^{2} = 81 - 72 x + 16 x^{2}

= 6 (16 x^{2} - 72 x + 81)

Distribute parentheses

= 6 \cdot 81 + 6 (- 72 x) + 6 \cdot 16 x^{2}

Apply minus-plus rules

+ (- a) = - a

= 6 \cdot 81 - 6 \cdot 72 x + 6 \cdot 16 x^{2}

Simplify

6 \cdot 81 - 6 \cdot 72 x + 6 \cdot 16 x^{2} : 486 - 432 x + 96 x^{2}

= 486 - 432 x + 96 x^{2}

Rewrite in standard form

= 96 x^{2} - 432 x + 486

(6 - a^{2}) + (13 + a^{2})

\frac{( 1 - x ) d x}{x ^{2}}

s in g (\frac{π}{2} - x)

f (x^{2} + π)

7 t (1 + 2 t) + e^{- 2 t} cos (10 t)

What is expand 6/((9-4x)^{-2)} ?
The solution to expand 6/((9-4x)^{-2)} is 96x^2-432x+486