What is expand (1/2-x^2)^4 ?

The solution to expand (1/2-x^2)^4 is 1/16-(x^2)/2+(3x^4)/2-2x^6+x^8

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expand (1/2-x^2)^4

expand

(\frac{1}{2} - x^{2})^{4}

\frac{1}{16} - \frac{x ^{2}}{2} + \frac{3 x ^{4}}{2} - 2 x^{6} + x^{8}

Solution steps

(\frac{1}{2} - x^{2})^{4}

Apply binomial theorem:

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

a = \frac{1}{2}, b = - x^{2}

= i = 0 \sum 4 (i 4) (\frac{1}{2})^{(4 - i)} (- x^{2})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (\frac{1}{2})^{4} (- x^{2})^{0} : \frac{1}{16}

Simplify

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

Simplify

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

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (\frac{1}{2})^{0} (- x^{2})^{4} : x^{8}

= \frac{1}{16} - \frac{x ^{2}}{2} + \frac{3 x ^{4}}{2} - 2 x^{6} + x^{8}

x (x + Δ x)

(x - 4) (ln (3 x)) d x

A (5, 1) B (7, - 7)

1 + \frac{k ( 0.3679 z + 0.2642 )}{( z - 0.3679 ) ( z - 1 )}

(y - x^{3}) d x + (y^{3} + x) d y

What is expand (1/2-x^2)^4 ?
The solution to expand (1/2-x^2)^4 is 1/16-(x^2)/2+(3x^4)/2-2x^6+x^8