What is expand (sin(x)+cos^2(x))^3 ?

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

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expand (sin(x)+cos^2(x))^3

expand

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

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

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

sin^{3} (x) + 3 sin^{2} (x) cos^{2} (x) + 3 sin (x) (cos^{2} (x))^{2} + (cos^{2} (x))^{3} : sin^{3} (x) + 3 sin^{2} (x) cos^{2} (x) + 3 cos^{4} (x) sin (x) + cos^{6} (x)

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

(x - 3) (2 x^{z} - x + 5)

\frac{( 3 x y )}{( x \cdot y ^{2} )}

(x^{2} + 4 x + 8)^{2} - 3 x (x^{2} + 4 x + 8) + 2 x^{2}

16 x y^{3} - 64 x y

\frac{( 3 - x )}{( 4 x - 12 )}

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