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

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

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expand (a+2b)^5

expand

(a + 2 b)^{5}

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

Solution steps

(a + 2 b)^{5}

Apply binomial theorem:

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

a = a, b = 2 b

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

\frac{( x ^{n} - 1 )}{( x - 1 )}

2 x^{2} - 5 x y + 3 y^{2}

arcsin (\frac{( 1 + x ^{2} )}{2})

\frac{2 ^{- 3} x ^{5} y ^{6} m ^{13}}{2 x ^{5} y ^{- 6} d ^{- 1}}

10 x^{2} \cdot y^{3} - 5 x^{2} \cdot y^{2} + 15 x^{3} \cdot y^{3}

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