What is expand (4(x-h)^2-4x)/h ?

The solution to expand (4(x-h)^2-4x)/h is (4x^2)/h-8x+4h-(4x)/h

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expand (4(x-h)^2-4x)/h

expand

\frac{4 ( x - h ) ^{2} - 4 x}{h}

\frac{4 x ^{2}}{h} - 8 x + 4 h - \frac{4 x}{h}

Solution steps

\frac{4 ( x - h ) ^{2} - 4 x}{h}

(x - h)^{2} = x^{2} - 2 x h + h^{2}

= \frac{4 ( x ^{2} - 2 x h + h ^{2} ) - 4 x}{h}

Expand

4 (x^{2} - 2 x h + h^{2}) - 4 x : 4 x^{2} - 8 x h + 4 h^{2} - 4 x

= \frac{4 x ^{2} - 8 x h + 4 h ^{2} - 4 x}{h}

Apply the fraction rule:

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

\frac{4 x ^{2} - 8 x h + 4 h ^{2} - 4 x}{h} = \frac{4 x ^{2}}{h} - \frac{8 x h}{h} + \frac{4 h ^{2}}{h} - \frac{4 x}{h}

= \frac{4 x ^{2}}{h} - \frac{8 x h}{h} + \frac{4 h ^{2}}{h} - \frac{4 x}{h}

Cancel

\frac{8 x h}{h} : 8 x

= \frac{4 x ^{2}}{h} - 8 x + \frac{4 h ^{2}}{h} - \frac{4 x}{h}

Cancel

\frac{4 h ^{2}}{h} : 4 h

= \frac{4 x ^{2}}{h} - 8 x + 4 h - \frac{4 x}{h}

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What is expand (4(x-h)^2-4x)/h ?
The solution to expand (4(x-h)^2-4x)/h is (4x^2)/h-8x+4h-(4x)/h