What is expand (2x-4y)^5 ?

The solution to expand (2x-4y)^5 is 32x^5-320x^4y+1280x^3y^2-2560x^2y^3+2560xy^4-1024y^5

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expand (2x-4y)^5

expand

(2 x - 4 y)^{5}

32 x^{5} - 320 x^{4} y + 1280 x^{3} y^{2} - 2560 x^{2} y^{3} + 2560 x y^{4} - 1024 y^{5}

Solution steps

(2 x - 4 y)^{5}

Apply binomial theorem:

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

a = 2 x, b = - 4 y

= i = 0 \sum 5 (i 5) (2 x)^{(5 - i)} (- 4 y)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 x)^{5} (- 4 y)^{0} : 32 x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 x)^{4} (- 4 y)^{1} : - 320 x^{4} y

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 x)^{3} (- 4 y)^{2} : 1280 x^{3} y^{2}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 x)^{2} (- 4 y)^{3} : - 2560 x^{2} y^{3}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 x)^{1} (- 4 y)^{4} : 2560 x y^{4}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 x)^{0} (- 4 y)^{5} : - 1024 y^{5}

= 32 x^{5} - 320 x^{4} y + 1280 x^{3} y^{2} - 2560 x^{2} y^{3} + 2560 x y^{4} - 1024 y^{5}

(x^{3} - 1)^{- 2}

2 (x + 6)

(6^{2})^{5}

(- 3 - 6 i) - (- 5 + 6 i)

8 (2 r + 5 s - 5)

What is expand (2x-4y)^5 ?
The solution to expand (2x-4y)^5 is 32x^5-320x^4y+1280x^3y^2-2560x^2y^3+2560xy^4-1024y^5