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

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

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expand (x^2-4)^4

expand

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

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

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

- 1 0^{- 3}

(a + b + 1)^{2} - (a + b + 1) (x - 2) + (a + b + 1)

- 1^{- \frac{1}{3}}

4 (2 x + 3) + 4 (3 x + 2)

\frac{3}{5} \div 6

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