What is expand (9cos(t)sin(t)+9cos^2(t))^2 ?

The solution to expand (9cos(t)sin(t)+9cos^2(t))^2 is 81cos^2(t)sin(2t)+81cos^2(t)

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expand (9cos(t)sin(t)+9cos^2(t))^2

expand

(9 cos (t) sin (t) + 9 cos^{2} (t))^{2}

81 cos^{2} (t) sin (2 t) + 81 cos^{2} (t)

Solution steps

(9 cos (t) sin (t) + 9 cos^{2} (t))^{2}

Apply Perfect Square Formula:

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

(9 cos (t) sin (t) + 9 cos^{2} (t))^{2} = (9 cos (t) sin (t))^{2} + 2 \cdot 9 cos (t) sin (t) \cdot 9 cos^{2} (t) + (9 cos^{2} (t))^{2}

= (9 cos (t) sin (t))^{2} + 2 \cdot 9 cos (t) sin (t) \cdot 9 cos^{2} (t) + (9 cos^{2} (t))^{2}

Simplify

(9 cos (t) sin (t))^{2} + 2 \cdot 9 cos (t) sin (t) \cdot 9 cos^{2} (t) + (9 cos^{2} (t))^{2} : 81 cos^{2} (t) (sin (2 t) + 1)

= 81 cos^{2} (t) (sin (2 t) + 1)

Apply the distributive law:

a (b + c) = ab + a c

81 cos^{2} (t) (sin (2 t) + 1) = 81 cos^{2} (t) sin (2 t) + 81 cos^{2} (t) \cdot 1

= 81 cos^{2} (t) sin (2 t) + 81 cos^{2} (t) \cdot 1

Multiply the numbers:

81 \cdot 1 = 81

= 81 cos^{2} (t) sin (2 t) + 81 cos^{2} (t)

- \frac{( 5 x ^{2} + 3 x + 17 )}{( x - 1 ) ( x ^{2} + 4 )}

\frac{( - 7 s + 27 )}{2 ( s ^{2} - 2 s + 5 )}

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

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(x - 17)^{2}

What is expand (9cos(t)sin(t)+9cos^2(t))^2 ?
The solution to expand (9cos(t)sin(t)+9cos^2(t))^2 is 81cos^2(t)sin(2t)+81cos^2(t)