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}

\frac{4 x ^{10}}{4 x ^{7}}

(x + 1) (x - 5)

(2 + x) (2 - x)

(x + a)^{2}

\frac{x - 4}{x ^{2} - 16}

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