What is expand (x+h)^4 ?

The solution to expand (x+h)^4 is x^4+4x^3h+6x^2h^2+4xh^3+h^4

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expand (x+h)^4

expand

(x + h)^{4}

x^{4} + 4 x^{3} h + 6 x^{2} h^{2} + 4 x h^{3} + h^{4}

Solution steps

(x + h)^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x, b = h

= i = 0 \sum 4 (i 4) x^{(4 - i)} h^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} h^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} h^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} h^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} h^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} h^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} x^{4} h^{0} : x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} h^{1} : 4 x^{3} h

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} h^{2} : 6 x^{2} h^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} h^{3} : 4 x h^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} h^{4} : h^{4}

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

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What is expand (x+h)^4 ?
The solution to expand (x+h)^4 is x^4+4x^3h+6x^2h^2+4xh^3+h^4