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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (m+2b)^5

expand

(m + 2 b)^{5}

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

Solution steps

(m + 2 b)^{5}

Apply binomial theorem:

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

a = m, b = 2 b

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

x^{3} + a^{3}

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

9 x^{2} - y^{2} + 4 y - 4

49 m^{2} - 16 x^{4}

\frac{x}{( a - a ^{2} - x ^{2} )}

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