What is expand (a+x)^5 ?

The solution to expand (a+x)^5 is a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5

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expand (a+x)^5

expand

(a + x)^{5}

a^{5} + 5 a^{4} x + 10 a^{3} x^{2} + 10 a^{2} x^{3} + 5 a x^{4} + x^{5}

Solution steps

(a + x)^{5}

Apply binomial theorem:

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

a = a, b = x

= i = 0 \sum 5 (i 5) a^{(5 - i)} x^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} a^{5} x^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} a^{4} x^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} a^{3} x^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} a^{2} x^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} a^{1} x^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} a^{0} x^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} a^{5} x^{0} : a^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} a^{4} x^{1} : 5 a^{4} x

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} a^{3} x^{2} : 10 a^{3} x^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} a^{2} x^{3} : 10 a^{2} x^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} a^{1} x^{4} : 5 a x^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} a^{0} x^{5} : x^{5}

= a^{5} + 5 a^{4} x + 10 a^{3} x^{2} + 10 a^{2} x^{3} + 5 a x^{4} + x^{5}

e^{x} (- e^{x})

39 - 5

n^{l o g_{4} (2)}

\frac{2}{\frac{8}{3}}

1 - \frac{8}{17}

What is expand (a+x)^5 ?
The solution to expand (a+x)^5 is a^5+5a^4x+10a^3x^2+10a^2x^3+5ax^4+x^5