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

The solution to expand (3sin(x)+3cos(x))^2 is 9sin(2x)+9

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

expand

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

9 sin (2 x) + 9

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(3 sin (x))^{2} + 2 \cdot 3 sin (x) \cdot 3 cos (x) + (3 cos (x))^{2} : 9 (sin (2 x) + 1)

= 9 (sin (2 x) + 1)

Apply the distributive law:

a (b + c) = ab + a c

9 (sin (2 x) + 1) = 9 sin (2 x) + 9 \cdot 1

= 9 sin (2 x) + 9 \cdot 1

Multiply the numbers:

9 \cdot 1 = 9

= 9 sin (2 x) + 9

5 (x + Δ x)^{2}

\frac{x ^{2}}{4 π} + \frac{( 57 - x ) ^{2}}{16}

e^{x} (e^{x} - 1)

\frac{4}{x ( x + 17 )}

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

What is expand (3sin(x)+3cos(x))^2 ?
The solution to expand (3sin(x)+3cos(x))^2 is 9sin(2x)+9