What is expand (x+y)^5 ?

The solution to expand (x+y)^5 is x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5

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expand (x+y)^5

expand

(x + y)^{5}

x^{5} + 5 x^{4} y + 10 x^{3} y^{2} + 10 x^{2} y^{3} + 5 x y^{4} + y^{5}

Solution steps

(x + y)^{5}

Apply binomial theorem:

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

a = x, b = y

= i = 0 \sum 5 (i 5) x^{(5 - i)} y^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} y^{0} : x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} y^{1} : 5 x^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} y^{2} : 10 x^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} y^{3} : 10 x^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} y^{4} : 5 x y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} y^{5} : y^{5}

= x^{5} + 5 x^{4} y + 10 x^{3} y^{2} + 10 x^{2} y^{3} + 5 x y^{4} + y^{5}

(x + y)^{6}

\frac{8 x ^{6} - 10 x ^{4} - 12 x ^{3}}{- 4 x ^{2}}

- x^{2} - 4

a^{3} + 27

\frac{225}{180}

What is expand (x+y)^5 ?
The solution to expand (x+y)^5 is x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5