What is expand ((1-a^2x)^2)/(b^3x) ?

The solution to expand ((1-a^2x)^2)/(b^3x) is 1/(b^3x)-(2a^2)/(b^3)+(a^4x)/(b^3)

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expand ((1-a^2x)^2)/(b^3x)

expand

\frac{( 1 - a ^{2} x ) ^{2}}{b ^{3} x}

\frac{1}{b ^{3} x} - \frac{2 a ^{2}}{b ^{3}} + \frac{a ^{4} x}{b ^{3}}

Solution steps

\frac{( 1 - a ^{2} x ) ^{2}}{b ^{3} x}

(1 - a^{2} x)^{2} = 1 - 2 a^{2} x + a^{4} x^{2}

= \frac{1 - 2 a ^{2} x + a ^{4} x ^{2}}{b ^{3} x}

Apply the fraction rule:

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

\frac{1 - 2 a ^{2} x + a ^{4} x ^{2}}{b ^{3} x} = \frac{1}{b ^{3} x} - \frac{2 a ^{2} x}{b ^{3} x} + \frac{a ^{4} x ^{2}}{b ^{3} x}

= \frac{1}{b ^{3} x} - \frac{2 a ^{2} x}{b ^{3} x} + \frac{a ^{4} x ^{2}}{b ^{3} x}

Cancel

\frac{2 a ^{2} x}{b ^{3} x} : \frac{2 a ^{2}}{b ^{3}}

= \frac{1}{b ^{3} x} - \frac{2 a ^{2}}{b ^{3}} + \frac{a ^{4} x ^{2}}{b ^{3} x}

Cancel

\frac{a ^{4} x ^{2}}{b ^{3} x} : \frac{a ^{4} x}{b ^{3}}

= \frac{1}{b ^{3} x} - \frac{2 a ^{2}}{b ^{3}} + \frac{a ^{4} x}{b ^{3}}

(3 x y^{2} + 20 x^{2} y^{3}) d y

\frac{x + 3}{x ( 3 - x )}

\frac{3 ( 10 + 102 )}{14}

(x^{42})^{2}

27 \cdot 21

What is expand ((1-a^2x)^2)/(b^3x) ?
The solution to expand ((1-a^2x)^2)/(b^3x) is 1/(b^3x)-(2a^2)/(b^3)+(a^4x)/(b^3)