What is expand (2x-y)^5 ?

The solution to expand (2x-y)^5 is 32x^5-80x^4y+80x^3y^2-40x^2y^3+10xy^4-y^5

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expand (2x-y)^5

expand

(2 x - y)^{5}

32 x^{5} - 80 x^{4} y + 80 x^{3} y^{2} - 40 x^{2} y^{3} + 10 x y^{4} - y^{5}

Solution steps

(2 x - y)^{5}

Apply binomial theorem:

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

a = 2 x, b = - y

= i = 0 \sum 5 (i 5) (2 x)^{(5 - i)} (- y)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 x)^{5} (- y)^{0} : 32 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 x)^{4} (- y)^{1} : - 80 x^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 x)^{3} (- y)^{2} : 80 x^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 x)^{2} (- y)^{3} : - 40 x^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 x)^{1} (- y)^{4} : 10 x y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 x)^{0} (- y)^{5} : - y^{5}

= 32 x^{5} - 80 x^{4} y + 80 x^{3} y^{2} - 40 x^{2} y^{3} + 10 x y^{4} - y^{5}

\frac{- 3}{- 4}

\frac{300}{180}

\frac{sin ( x )}{cos ( x )} + \frac{cos ( x )}{1 + sin ( x )}

3 x^{0}

\frac{2 a + 3}{4 a} - \frac{a - 2}{8 a}

What is expand (2x-y)^5 ?
The solution to expand (2x-y)^5 is 32x^5-80x^4y+80x^3y^2-40x^2y^3+10xy^4-y^5