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

The solution to expand (x^2-2y)^4 is x^8-8x^6y+24x^4y^2-32x^2y^3+16y^4

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expand (x^2-2y)^4

expand

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

x^{8} - 8 x^{6} y + 24 x^{4} y^{2} - 32 x^{2} y^{3} + 16 y^{4}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} (- 2 y)^{0} : x^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (- 2 y)^{1} : - 8 x^{6} y

Simplify

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

Simplify

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

Simplify

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

= x^{8} - 8 x^{6} y + 24 x^{4} y^{2} - 32 x^{2} y^{3} + 16 y^{4}

(4 r - 3 u - 6 t) + (3 r + 5 u + 2 t)

- 1. 8^{2}

44 + 99

a r g (1 + i)

What is expand (x^2-2y)^4 ?
The solution to expand (x^2-2y)^4 is x^8-8x^6y+24x^4y^2-32x^2y^3+16y^4