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

The solution to expand (x-2y)^4 is x^4-8x^3y+24x^2y^2-32xy^3+16y^4

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expand (x-2y)^4

expand

(x - 2 y)^{4}

x^{4} - 8 x^{3} y + 24 x^{2} y^{2} - 32 x y^{3} + 16 y^{4}

Solution steps

(x - 2 y)^{4}

Apply binomial theorem:

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

a = x, b = - 2 y

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} x^{3} (- 2 y)^{1} : - 8 x^{3} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} x^{2} (- 2 y)^{2} : 24 x^{2} y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} x^{1} (- 2 y)^{3} : - 32 x y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} x^{0} (- 2 y)^{4} : 16 y^{4}

= x^{4} - 8 x^{3} y + 24 x^{2} y^{2} - 32 x y^{3} + 16 y^{4}

\frac{x - 2}{x ^{2} + x - 6}

\frac{- 24 - 12 i}{3 + 9 i}

\frac{1}{1} + \frac{1}{2}

(7 + 9 i) (7 + 4 i)

x (1 - x)

What is expand (x-2y)^4 ?
The solution to expand (x-2y)^4 is x^4-8x^3y+24x^2y^2-32xy^3+16y^4