What is expand (x+2)^5 ?

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

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expand (x+2)^5

expand

(x + 2)^{5}

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

Solution steps

(x + 2)^{5}

Apply binomial theorem:

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

a = x, b = 2

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

- 100

\frac{1}{5}

(s - 1)^{2}

- 2^{0}

ln (e^{- x})

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