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

The solution to expand (2z^2-2x)^4 is 16z^8-64z^6x+96z^4x^2-64z^2x^3+16x^4

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expand (2z^2-2x)^4

expand

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

16 z^{8} - 64 z^{6} x + 96 z^{4} x^{2} - 64 z^{2} x^{3} + 16 x^{4}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 z^{2})^{4} (- 2 x)^{0} : 16 z^{8}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 z^{2})^{3} (- 2 x)^{1} : - 64 z^{6} x

Simplify

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

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 z^{2})^{1} (- 2 x)^{3} : - 64 z^{2} x^{3}

Simplify

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

= 16 z^{8} - 64 z^{6} x + 96 z^{4} x^{2} - 64 z^{2} x^{3} + 16 x^{4}

\frac{84}{36}

(- x + 1) (x - 1)

\frac{84}{96}

2.2 e - 16

5 \times 6.022 \times 1 0^{23}

What is expand (2z^2-2x)^4 ?
The solution to expand (2z^2-2x)^4 is 16z^8-64z^6x+96z^4x^2-64z^2x^3+16x^4