What is expand (1+sin(x))^3 ?

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

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expand (1+sin(x))^3

expand

(1 + sin (x))^{3}

1 + 3 sin (x) + 3 sin^{2} (x) + sin^{3} (x)

Solution steps

(1 + sin (x))^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(1 + sin (x))^{3} = 1^{3} + 3 \cdot 1^{2} sin (x) + 3 \cdot 1 \cdot sin^{2} (x) + sin^{3} (x)

= 1^{3} + 3 \cdot 1^{2} sin (x) + 3 \cdot 1 \cdot sin^{2} (x) + sin^{3} (x)

Simplify

1^{3} + 3 \cdot 1^{2} sin (x) + 3 \cdot 1 \cdot sin^{2} (x) + sin^{3} (x) : 1 + 3 sin (x) + 3 sin^{2} (x) + sin^{3} (x)

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

2 (5 + 7)

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

\frac{( x ^{2} + x ^{2} )}{( 2 - x ^{2} )}

l im x \Rightarrow 0 (1 + x) - 2 - 1 x

\frac{x ^{2} y ^{''} ( x ) + x y ^{'} ( x ) - y ( x + 1 ) + 1}{( x + 1 ) x ^{2}}

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