What is expand ((2+cos(u)sin(u)))^2 ?

The solution to expand ((2+cos(u)sin(u)))^2 is 4+4cos(u)sin(u)+cos^2(u)sin^2(u)

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expand ((2+cos(u)sin(u)))^2

expand

((2 + cos (u) sin (u)))^{2}

4 + 4 cos (u) sin (u) + cos^{2} (u) sin^{2} (u)

Solution steps

(2 + cos (u) sin (u))^{2}

Simplify

(2 + cos (u) sin (u)) : 2 + cos (u) sin (u)

= (2 + cos (u) sin (u))^{2}

Apply Perfect Square Formula:

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

(2 + cos (u) sin (u))^{2} = 2^{2} + 2 \cdot 2 cos (u) sin (u) + (cos (u) sin (u))^{2}

= 2^{2} + 2 \cdot 2 cos (u) sin (u) + (cos (u) sin (u))^{2}

Simplify

2^{2} + 2 \cdot 2 cos (u) sin (u) + (cos (u) sin (u))^{2} : 4 + 4 cos (u) sin (u) + cos^{2} (u) sin^{2} (u)

= 4 + 4 cos (u) sin (u) + cos^{2} (u) sin^{2} (u)

\frac{10 x + 9}{3 ( x + 1 ) ( 2 x + 3 )}

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

\frac{4 x + 2}{( x - 2 ) ( 3 x + 4 )}

4 (y^{4} + 3 y^{2}) + 1

What is expand ((2+cos(u)sin(u)))^2 ?
The solution to expand ((2+cos(u)sin(u)))^2 is 4+4cos(u)sin(u)+cos^2(u)sin^2(u)