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

The solution to expand (2*(-x^4+(h+x)^4))/h is 8x^3+12x^2h+8xh^2+2h^3

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

expand

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

8 x^{3} + 12 x^{2} h + 8 x h^{2} + 2 h^{3}

Solution steps

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

Factor

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

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

Cancel the common factor:

h

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

Expand

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

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

Expand

(2 x^{2} + 2 x h + h^{2}) (2 x + h) : 4 x^{3} + 6 x^{2} h + 4 x h^{2} + h^{3}

= 2 (4 x^{3} + 6 x^{2} h + 4 x h^{2} + h^{3})

Expand

2 (4 x^{3} + 6 x^{2} h + 4 x h^{2} + h^{3}) : 8 x^{3} + 12 x^{2} h + 8 x h^{2} + 2 h^{3}

= 8 x^{3} + 12 x^{2} h + 8 x h^{2} + 2 h^{3}

(\frac{a + b}{2}) (\frac{c - d}{2})

(k + 1)! (k + 1)

a (1, 2, 0) b (1, - 1, 2) c (0, 1, 1)

\frac{200 s}{( 9 s + s ^{2} + 10 ) ( s ^{2} + 400 )}

\frac{( 1 - x )}{( x + 1 ) ^{2}}

What is expand (2*(-x^4+(h+x)^4))/h ?
The solution to expand (2*(-x^4+(h+x)^4))/h is 8x^3+12x^2h+8xh^2+2h^3