What is expand (1+2a)^5 ?

The solution to expand (1+2a)^5 is 1+10a+40a^2+80a^3+80a^4+32a^5

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expand (1+2a)^5

expand

(1 + 2 a)^{5}

1 + 10 a + 40 a^{2} + 80 a^{3} + 80 a^{4} + 32 a^{5}

Solution steps

(1 + 2 a)^{5}

Apply binomial theorem:

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

a = 1, b = 2 a

= i = 0 \sum 5 (i 5) \cdot 1^{(5 - i)} (2 a)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 1^{5} (2 a)^{0} : 1

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (2 a)^{2} : 40 a^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (2 a)^{3} : 80 a^{3}

Simplify

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

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} (2 a)^{5} : 32 a^{5}

= 1 + 10 a + 40 a^{2} + 80 a^{3} + 80 a^{4} + 32 a^{5}

b^{2} c^{0}

\frac{( ( - sin ( x ) ) - ( \frac{c o s ( x )}{x} ) )}{cos ^{2} ( x )}

- \frac{56}{9} y - \frac{5}{6}

\frac{5 x}{3 + ( x - \frac{1}{2} ) - 2 x}

(x y^{- 1}) x^{- 3} y^{0}

What is expand (1+2a)^5 ?
The solution to expand (1+2a)^5 is 1+10a+40a^2+80a^3+80a^4+32a^5