What is expand ((2b+3a)(-6b+3a))/(b^2) ?

The solution to expand ((2b+3a)(-6b+3a))/(b^2) is -12-(12a)/b+(9a^2)/(b^2)

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expand ((2b+3a)(-6b+3a))/(b^2)

expand

\frac{( 2 b + 3 a ) ( - 6 b + 3 a )}{b ^{2}}

- 12 - \frac{12 a}{b} + \frac{9 a ^{2}}{b ^{2}}

Solution steps

\frac{( 2 b + 3 a ) ( - 6 b + 3 a )}{b ^{2}}

Expand

(2 b + 3 a) (- 6 b + 3 a) : - 12 b^{2} - 12 ba + 9 a^{2}

= \frac{- 12 b ^{2} - 12 ba + 9 a ^{2}}{b ^{2}}

Apply the fraction rule:

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

\frac{- 12 b ^{2} - 12 ba + 9 a ^{2}}{b ^{2}} = - \frac{12 b ^{2}}{b ^{2}} - \frac{12 ba}{b ^{2}} + \frac{9 a ^{2}}{b ^{2}}

= - \frac{12 b ^{2}}{b ^{2}} - \frac{12 ba}{b ^{2}} + \frac{9 a ^{2}}{b ^{2}}

Cancel

\frac{12 b ^{2}}{b ^{2}} : 12

= - 12 - \frac{12 ba}{b ^{2}} + \frac{9 a ^{2}}{b ^{2}}

Cancel

\frac{12 ba}{b ^{2}} : \frac{12 a}{b}

= - 12 - \frac{12 a}{b} + \frac{9 a ^{2}}{b ^{2}}

\frac{4}{5 ( x + 1 )}

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f (2, 4, - 3, 3)

\frac{1}{( 4 s ^{4} - 4 s + 5 ) ^{2}}

2 (e^{x} (A cos (x) + B sin (x)))

What is expand ((2b+3a)(-6b+3a))/(b^2) ?
The solution to expand ((2b+3a)(-6b+3a))/(b^2) is -12-(12a)/b+(9a^2)/(b^2)