What is expand ([(x+h)^3x]-x^3-x)/h ?

The solution to expand ([(x+h)^3x]-x^3-x)/h is (x^4)/h+3x^3+3x^2h+xh^2-(x^3)/h-x/h

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expand ([(x+h)^3x]-x^3-x)/h

expand

\frac{[ ( x + h ) ^{3} x ] - x ^{3} - x}{h}

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

Solution steps

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

Remove parentheses:

(a) = a

= \frac{( x + h ) ^{3} x - x ^{3} - x}{h}

(x + h)^{3} = x^{3} + 3 x^{2} h + 3 x h^{2} + h^{3}

= \frac{x ( x ^{3} + 3 x ^{2} h + 3 x h ^{2} + h ^{3} ) - x ^{3} - x}{h}

Expand

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

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

Apply the fraction rule:

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

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

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

Cancel

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

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

Cancel

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

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

Cancel

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

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

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\frac{2}{( z - 2 j ) ( z + j )}

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(\frac{v ^{1} - v}{a})^{2}

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