What is expand (a+b)^7 ?

The solution to expand (a+b)^7 is a^7+7a^6b+21a^5b^2+35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7

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expand (a+b)^7

expand

(a + b)^{7}

a^{7} + 7 a^{6} b + 21 a^{5} b^{2} + 35 a^{4} b^{3} + 35 a^{3} b^{4} + 21 a^{2} b^{5} + 7 a b^{6} + b^{7}

Solution steps

(a + b)^{7}

Apply binomial theorem:

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

a = a, b = b

= i = 0 \sum 7 (i 7) a^{(7 - i)} b^{i}

Expand summation

= \frac{7 !}{0 ! ( 7 - 0 ) !} a^{7} b^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} a^{6} b^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} a^{5} b^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} a^{4} b^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} a^{3} b^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} a^{2} b^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} a^{1} b^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} a^{0} b^{7}

Simplify

\frac{7 !}{0 ! ( 7 - 0 ) !} a^{7} b^{0} : a^{7}

Simplify

\frac{7 !}{1 ! ( 7 - 1 ) !} a^{6} b^{1} : 7 a^{6} b

Simplify

\frac{7 !}{2 ! ( 7 - 2 ) !} a^{5} b^{2} : 21 a^{5} b^{2}

Simplify

\frac{7 !}{3 ! ( 7 - 3 ) !} a^{4} b^{3} : 35 a^{4} b^{3}

Simplify

\frac{7 !}{4 ! ( 7 - 4 ) !} a^{3} b^{4} : 35 a^{3} b^{4}

Simplify

\frac{7 !}{5 ! ( 7 - 5 ) !} a^{2} b^{5} : 21 a^{2} b^{5}

Simplify

\frac{7 !}{6 ! ( 7 - 6 ) !} a^{1} b^{6} : 7 a b^{6}

Simplify

\frac{7 !}{7 ! ( 7 - 7 ) !} a^{0} b^{7} : b^{7}

= a^{7} + 7 a^{6} b + 21 a^{5} b^{2} + 35 a^{4} b^{3} + 35 a^{3} b^{4} + 21 a^{2} b^{5} + 7 a b^{6} + b^{7}

- 1 \div 1

2 x \cdot 4 x

(s + 2) (s + 4)

\frac{x - y}{y - x}

What is expand (a+b)^7 ?
The solution to expand (a+b)^7 is a^7+7a^6b+21a^5b^2+35a^4b^3+35a^3b^4+21a^2b^5+7ab^6+b^7