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

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

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

expand

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

1 - 4 cos^{2} (x) + 6 cos^{4} (x) - 4 cos^{6} (x) + cos^{8} (x)

Solution steps

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

Apply binomial theorem:

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

a = 1, b = - cos^{2} (x)

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= 1 - 4 cos^{2} (x) + 6 cos^{4} (x) - 4 cos^{6} (x) + cos^{8} (x)

15 x yz (\frac{x ^{2} y z ^{3}}{3} + x^{4} y^{4} z - \frac{5 x}{3 z ^{3}})

\frac{1}{2} (1 - cos (x))

(5 x + 2 y = 8,) (2 x - 4 y = - 8)

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

A (- 3, - 2) y B (8, 3)

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