What is expand (2+x)^5 ?

The solution to expand (2+x)^5 is 32+80x+80x^2+40x^3+10x^4+x^5

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expand (2+x)^5

expand

(2 + x)^{5}

32 + 80 x + 80 x^{2} + 40 x^{3} + 10 x^{4} + x^{5}

Solution steps

(2 + x)^{5}

Apply binomial theorem:

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

a = 2, b = x

= i = 0 \sum 5 (i 5) \cdot 2^{(5 - i)} x^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 2^{5} x^{0} : 32

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 2^{4} x^{1} : 80 x

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 2^{3} x^{2} : 80 x^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 2^{2} x^{3} : 40 x^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 2^{1} x^{4} : 10 x^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 2^{0} x^{5} : x^{5}

= 32 + 80 x + 80 x^{2} + 40 x^{3} + 10 x^{4} + x^{5}

\frac{15 x ^{3} - 12 x ^{2} + 6 x}{3 x}

\frac{1}{2} (- 3)

\frac{1}{x} + 3

\frac{1}{x} - 2

\frac{12 a ^{3} b ^{3} c ^{4} + 18 ab c ^{3} - 24 a ^{2} b ^{2} c ^{8}}{6 a b ^{2} c ^{2}}

What is expand (2+x)^5 ?
The solution to expand (2+x)^5 is 32+80x+80x^2+40x^3+10x^4+x^5