What is expand (x^2(x+h)^2)/h ?

The solution to expand (x^2(x+h)^2)/h is (x^4)/h+2x^3+x^2h

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expand (x^2(x+h)^2)/h

expand

\frac{x ^{2} ( x + h ) ^{2}}{h}

\frac{x ^{4}}{h} + 2 x^{3} + x^{2} h

Solution steps

\frac{x ^{2} ( x + h ) ^{2}}{h}

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

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

Expand

x^{2} (x^{2} + 2 x h + h^{2}) : x^{4} + 2 x^{3} h + x^{2} h^{2}

= \frac{x ^{4} + 2 x ^{3} h + x ^{2} h ^{2}}{h}

Apply the fraction rule:

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

\frac{x ^{4} + 2 x ^{3} h + x ^{2} h ^{2}}{h} = \frac{x ^{4}}{h} + \frac{2 x ^{3} h}{h} + \frac{x ^{2} h ^{2}}{h}

= \frac{x ^{4}}{h} + \frac{2 x ^{3} h}{h} + \frac{x ^{2} h ^{2}}{h}

Cancel

\frac{2 x ^{3} h}{h} : 2 x^{3}

= \frac{x ^{4}}{h} + 2 x^{3} + \frac{x ^{2} h ^{2}}{h}

Cancel

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

= \frac{x ^{4}}{h} + 2 x^{3} + x^{2} h

- 4 (- \frac{π M}{2} + 5 (2 π - 4))

\frac{2 x - 5}{( x - 1 ) ( x - 4 )}

\frac{d ^{2}}{d x ^{2}} ((y) (4 x - 1))

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

(x - π)^{4}

What is expand (x^2(x+h)^2)/h ?
The solution to expand (x^2(x+h)^2)/h is (x^4)/h+2x^3+x^2h