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

The solution to expand (x^2-4y)^4 is x^8-16x^6y+96x^4y^2-256x^2y^3+256y^4

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expand (x^2-4y)^4

expand

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

x^{8} - 16 x^{6} y + 96 x^{4} y^{2} - 256 x^{2} y^{3} + 256 y^{4}

Solution steps

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

Apply binomial theorem:

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

a = x^{2}, b = - 4 y

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (- 4 y)^{1} : - 16 x^{6} y

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} (- 4 y)^{2} : 96 x^{4} y^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} (- 4 y)^{3} : - 256 x^{2} y^{3}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} (- 4 y)^{4} : 256 y^{4}

= x^{8} - 16 x^{6} y + 96 x^{4} y^{2} - 256 x^{2} y^{3} + 256 y^{4}

(2 (x + 1) - 4 (x + 3)) (2 (x + 1) - 4 (x + 3))

49 x^{2} - 56 x y + 16 y^{2}

x (3 x - 2)

5 - 45

- 2 x^{2} - 3

What is expand (x^2-4y)^4 ?
The solution to expand (x^2-4y)^4 is x^8-16x^6y+96x^4y^2-256x^2y^3+256y^4