What is expand (g+2)^5 ?

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

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expand (g+2)^5

expand

(g + 2)^{5}

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

Solution steps

(g + 2)^{5}

Apply binomial theorem:

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

a = g, b = 2

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

(k^{2} - 5 k - 2) (k^{2} + 2)

4 x (3 x - 2 y^{2})

2 + (- 4)

\frac{11}{7}

(2 x^{3} + 5 x - 3) + (4 x - 3 x^{2} + 2 x^{3})

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