What is expand (1-sin(x))^4 ?

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

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expand (1-sin(x))^4

expand

(1 - sin (x))^{4}

1 - 4 sin (x) + 6 sin^{2} (x) - 4 sin^{3} (x) + sin^{4} (x)

Solution steps

(1 - sin (x))^{4}

Apply binomial theorem:

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

a = 1, b = - sin (x)

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= 1 - 4 sin (x) + 6 sin^{2} (x) - 4 sin^{3} (x) + sin^{4} (x)

3 x - 15 x + 5

(4 x^{2} - 6)^{4}

[\frac{1}{( x - 1 ) ^{- 1}} - \frac{\frac{1}{1}}{( x - 2 ) ^{- 2}}]^{2}

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

\frac{\frac{b}{a}}{( - 3 )}

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