What is expand (1+2sin(2x))^2 ?

The solution to expand (1+2sin(2x))^2 is 1+4sin(2x)+4sin^2(2x)

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expand (1+2sin(2x))^2

expand

(1 + 2 sin (2 x))^{2}

1 + 4 sin (2 x) + 4 sin^{2} (2 x)

Solution steps

(1 + 2 sin (2 x))^{2}

Apply Perfect Square Formula:

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

(1 + 2 sin (2 x))^{2} = 1^{2} + 2 \cdot 1 \cdot 2 sin (2 x) + (2 sin (2 x))^{2}

= 1^{2} + 2 \cdot 1 \cdot 2 sin (2 x) + (2 sin (2 x))^{2}

Simplify

1^{2} + 2 \cdot 1 \cdot 2 sin (2 x) + (2 sin (2 x))^{2} : 1 + 4 sin (2 x) + 4 sin^{2} (2 x)

= 1 + 4 sin (2 x) + 4 sin^{2} (2 x)

2 (4 - 22)

cos (θ) (1 + sin (θ))

(cot (x) + 1) (2 (sin (x)) + 3)

(e^{2 x} + 2 e^{2 x} x) (e^{2 x})

π (r_{0} - a t)^{2}

What is expand (1+2sin(2x))^2 ?
The solution to expand (1+2sin(2x))^2 is 1+4sin(2x)+4sin^2(2x)