What is expand ((a+h)^4)/2 ?

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

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expand ((a+h)^4)/2

expand

\frac{( a + h ) ^{4}}{2}

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

Solution steps

\frac{( a + h ) ^{4}}{2}

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

= \frac{a ^{4} + 4 a ^{3} h + 6 a ^{2} h ^{2} + 4 a h ^{3} + h ^{4}}{2}

Apply the fraction rule:

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

\frac{a ^{4} + 4 a ^{3} h + 6 a ^{2} h ^{2} + 4 a h ^{3} + h ^{4}}{2} = \frac{a ^{4}}{2} + \frac{4 a ^{3} h}{2} + \frac{6 a ^{2} h ^{2}}{2} + \frac{4 a h ^{3}}{2} + \frac{h ^{4}}{2}

= \frac{a ^{4}}{2} + \frac{4 a ^{3} h}{2} + \frac{6 a ^{2} h ^{2}}{2} + \frac{4 a h ^{3}}{2} + \frac{h ^{4}}{2}

Divide the numbers:

\frac{4}{2} = 2

= \frac{a ^{4}}{2} + 2 a^{3} h + \frac{6 a ^{2} h ^{2}}{2} + \frac{4 a h ^{3}}{2} + \frac{h ^{4}}{2}

Divide the numbers:

\frac{6}{2} = 3

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

Divide the numbers:

\frac{4}{2} = 2

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

2 (y (y - 2))

\frac{x ^{3} - 1}{x ( 3 x ^{2} + 1 )}

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

\frac{( 3 x ^{2} + 4 x - 3 )}{x}

(1, 1, 1) X (- 1, - 10, 1)

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