What is expand 4+5(2sin(3x)-4cos(3x))^2 ?

The solution to expand 4+5(2sin(3x)-4cos(3x))^2 is 4+20sin^2(3x)-80cos(3x)sin(3x)+80cos^2(3x)

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expand 4+5(2sin(3x)-4cos(3x))^2

expand

4 + 5 (2 sin (3 x) - 4 cos (3 x))^{2}

4 + 20 sin^{2} (3 x) - 80 cos (3 x) sin (3 x) + 80 cos^{2} (3 x)

Solution steps

4 + 5 (2 sin (3 x) - 4 cos (3 x))^{2}

Expand

(2 sin (3 x) - 4 cos (3 x))^{2} : 4 sin^{2} (3 x) - 16 cos (3 x) sin (3 x) + 16 cos^{2} (3 x)

= 4 + 5 (4 sin^{2} (3 x) - 16 cos (3 x) sin (3 x) + 16 cos^{2} (3 x))

Apply the distributive law:

m (a + b + c) = ma + mb + m c

5 (4 sin^{2} (3 x) - 16 cos (3 x) sin (3 x) + 16 cos^{2} (3 x)) = 5 \cdot 4 sin^{2} (3 x) + 5 (- 16 cos (3 x) sin (3 x)) + 5 \cdot 16 cos^{2} (3 x)

= 4 + 5 \cdot 4 sin^{2} (3 x) + 5 (- 16 cos (3 x) sin (3 x)) + 5 \cdot 16 cos^{2} (3 x)

Simplify

5 \cdot 4 sin^{2} (3 x) + 5 (- 16 cos (3 x) sin (3 x)) + 5 \cdot 16 cos^{2} (3 x) : 20 sin^{2} (3 x) - 80 cos (3 x) sin (3 x) + 80 cos^{2} (3 x)

= 4 + 20 sin^{2} (3 x) - 80 cos (3 x) sin (3 x) + 80 cos^{2} (3 x)

(n) (n + 2) (n + 4) (n + 6) + 16

\frac{6 n - 3 - 24 n ^{2} + 44 n - 39}{2 ( 3 n - 2 )}

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

(x - 1 - x)^{2}

K (1 + A + \frac{- A - 2 B}{z} + B + \frac{B}{z ^{2}}) \cdot 0.01397

What is expand 4+5(2sin(3x)-4cos(3x))^2 ?
The solution to expand 4+5(2sin(3x)-4cos(3x))^2 is 4+20sin^2(3x)-80cos(3x)sin(3x)+80cos^2(3x)