What is expand (a+b)^6 ?

The solution to expand (a+b)^6 is a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6

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expand (a+b)^6

expand

(a + b)^{6}

a^{6} + 6 a^{5} b + 15 a^{4} b^{2} + 20 a^{3} b^{3} + 15 a^{2} b^{4} + 6 a b^{5} + b^{6}

Solution steps

(a + b)^{6}

Apply binomial theorem:

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

a = a, b = b

= i = 0 \sum 6 (i 6) a^{(6 - i)} b^{i}

Expand summation

= \frac{6 !}{0 ! ( 6 - 0 ) !} a^{6} b^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} a^{5} b^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} a^{4} b^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} a^{3} b^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} a^{2} b^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} a^{1} b^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} a^{0} b^{6}

Simplify

\frac{6 !}{0 ! ( 6 - 0 ) !} a^{6} b^{0} : a^{6}

Simplify

\frac{6 !}{1 ! ( 6 - 1 ) !} a^{5} b^{1} : 6 a^{5} b

Simplify

\frac{6 !}{2 ! ( 6 - 2 ) !} a^{4} b^{2} : 15 a^{4} b^{2}

Simplify

\frac{6 !}{3 ! ( 6 - 3 ) !} a^{3} b^{3} : 20 a^{3} b^{3}

Simplify

\frac{6 !}{4 ! ( 6 - 4 ) !} a^{2} b^{4} : 15 a^{2} b^{4}

Simplify

\frac{6 !}{5 ! ( 6 - 5 ) !} a^{1} b^{5} : 6 a b^{5}

Simplify

\frac{6 !}{6 ! ( 6 - 6 ) !} a^{0} b^{6} : b^{6}

= a^{6} + 6 a^{5} b + 15 a^{4} b^{2} + 20 a^{3} b^{3} + 15 a^{2} b^{4} + 6 a b^{5} + b^{6}

x (x + 2)

\frac{3}{15}

ln (e^{2 x})

\frac{x ^{2} - 9}{x + 3}

x \cdot x

What is expand (a+b)^6 ?
The solution to expand (a+b)^6 is a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6