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

The solution to expand (x/2-5y)^4 is (10000y^4+x^4}{16}+\frac{-5x^3y+75x^2y^2)/2-250xy^3

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expand (x/2-5y)^4

expand

(\frac{x}{2} - 5 y)^{4}

\frac{10000 y ^{4} + x ^{4}}{16} + \frac{- 5 x ^{3} y + 75 x ^{2} y ^{2}}{2} - 250 x y^{3}

Solution steps

(\frac{x}{2} - 5 y)^{4}

Apply binomial theorem:

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

a = \frac{x}{2}, b = - 5 y

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

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (\frac{x}{2})^{4} (- 5 y)^{0} : \frac{x ^{4}}{16}

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (\frac{x}{2})^{2} (- 5 y)^{2} : \frac{75 x ^{2} y ^{2}}{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (\frac{x}{2})^{1} (- 5 y)^{3} : - 250 x y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (\frac{x}{2})^{0} (- 5 y)^{4} : 625 y^{4}

= \frac{x ^{4}}{16} - \frac{5 x ^{3} y}{2} + \frac{75 x ^{2} y ^{2}}{2} - 250 x y^{3} + 625 y^{4}

Join

\frac{x ^{4}}{16} - \frac{5 x ^{3} y}{2} + \frac{75 x ^{2} y ^{2}}{2} - 250 x y^{3} + 625 y^{4} : \frac{10000 y ^{4} + x ^{4}}{16} + \frac{- 5 x ^{3} y + 75 x ^{2} y ^{2}}{2} - 250 x y^{3}

= \frac{10000 y ^{4} + x ^{4}}{16} + \frac{- 5 x ^{3} y + 75 x ^{2} y ^{2}}{2} - 250 x y^{3}

(1 + 3 i)^{4}

(cos (x) - x sin (x))^{2}

(x + y) (x + y)

\frac{2 x - 12}{( x - 4 ) ( x - 5 )}

(a - x)^{4}

What is expand (x/2-5y)^4 ?
The solution to expand (x/2-5y)^4 is (10000y^4+x^4}{16}+\frac{-5x^3y+75x^2y^2)/2-250xy^3