What is expand (5x-2y^3)^4 ?

The solution to expand (5x-2y^3)^4 is 625x^4-1000x^3y^3+600x^2y^6-160xy^9+16y^{12}

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expand (5x-2y^3)^4

expand

(5 x - 2 y^{3})^{4}

625 x^{4} - 1000 x^{3} y^{3} + 600 x^{2} y^{6} - 160 x y^{9} + 16 y^{12}

Solution steps

(5 x - 2 y^{3})^{4}

Apply binomial theorem:

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

a = 5 x, b = - 2 y^{3}

= i = 0 \sum 4 (i 4) (5 x)^{(4 - i)} (- 2 y^{3})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (5 x)^{4} (- 2 y^{3})^{0} : 625 x^{4}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (5 x)^{3} (- 2 y^{3})^{1} : - 1000 x^{3} y^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (5 x)^{2} (- 2 y^{3})^{2} : 600 x^{2} y^{6}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (5 x)^{1} (- 2 y^{3})^{3} : - 160 x y^{9}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (5 x)^{0} (- 2 y^{3})^{4} : 16 y^{12}

= 625 x^{4} - 1000 x^{3} y^{3} + 600 x^{2} y^{6} - 160 x y^{9} + 16 y^{12}

e^{- 2 t} cos (3 t) - t^{2} e^{- 2 t}

2 5^{2} - 2 4^{2}

\frac{1}{7} + \frac{1}{5}

\frac{1}{27}

What is expand (5x-2y^3)^4 ?
The solution to expand (5x-2y^3)^4 is 625x^4-1000x^3y^3+600x^2y^6-160xy^9+16y^{12}