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

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

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expand (-2x+5y)^4

expand

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

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

Solution steps

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

Apply binomial theorem:

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

a = - 2 x, b = 5 y

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

5 x^{2} + 7 x^{2}

(9 + 5 i) - (8 - 10 i)

(a^{2} + 2)^{3}

- 4 i (2 + 3 i)

- 6 b - 18 + 14 b

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