What is ((a+h)^3-a^3)/h ?

The solution to ((a+h)^3-a^3)/h is h^2+3a^2+3ha

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simplify ((a+h)^3-a^3)/h

simplify

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

h^{2} + 3 a^{2} + 3 ha

Solution steps

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

Expand

(a + h)^{3} - a^{3} : h^{3} + 3 h a^{2} + 3 a h^{2}

= \frac{h ^{3} + 3 h a ^{2} + 3 a h ^{2}}{h}

Factor

h^{3} + 3 h a^{2} + 3 h^{2} a : h (h^{2} + 3 a^{2} + 3 ha)

= \frac{h ( h ^{2} + 3 a ^{2} + 3 ha )}{h}

Cancel the common factor:

h

= h^{2} + 3 a^{2} + 3 ha

b + 2 (b + 2 b)

24 y + 18 y^{2}

\frac{x ^{2} - 1}{x ^{2} - x - 2}

(- 12 + 10 i) - (- 8 + i)

(x + 2) (2 x - 5)