What is expand (a+b)^5 ?

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

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expand (a+b)^5

expand

(a + b)^{5}

a^{5} + 5 a^{4} b + 10 a^{3} b^{2} + 10 a^{2} b^{3} + 5 a b^{4} + b^{5}

Solution steps

(a + b)^{5}

Apply binomial theorem:

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

a = a, b = b

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} a^{3} b^{2} : 10 a^{3} b^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} a^{2} b^{3} : 10 a^{2} b^{3}

Simplify

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

Simplify

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

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

(x - 3) (x - 3)

(s + 1)^{3}

(1 + x)^{2}

- 1^{0}

4 x^{2} y + 8 x y^{2}

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