What is factor (x+h)^3-x^3 ?

The solution to factor (x+h)^3-x^3 is h(3x^2+3xh+h^2)

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factor (x+h)^3-x^3

factor

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

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

Solution steps

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

Apply Difference of Cubes Formula:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

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

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

Refine

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

Expand

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

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

3 x^{2} - x - 2 = - 2

2 x^{2} + 50 y^{2} - 20 x y

(- \frac{7}{4}) - \frac{2}{9}

\frac{1 - 6 i}{3 i}

\frac{( 1 + x ) ^{2}}{5} = \frac{2 x + 4}{25} + \frac{x ^{2}}{5} + \frac{1}{5}

What is factor (x+h)^3-x^3 ?
The solution to factor (x+h)^3-x^3 is h(3x^2+3xh+h^2)