What is expand (2sin(θ)+2cos(θ))^2 ?

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

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expand (2sin(θ)+2cos(θ))^2

expand

(2 sin (θ) + 2 cos (θ))^{2}

4 sin (2 θ) + 4

Solution steps

(2 sin (θ) + 2 cos (θ))^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= 4 (sin (2 θ) + 1)

Apply the distributive law:

a (b + c) = ab + a c

4 (sin (2 θ) + 1) = 4 sin (2 θ) + 4 \cdot 1

= 4 sin (2 θ) + 4 \cdot 1

Multiply the numbers:

4 \cdot 1 = 4

= 4 sin (2 θ) + 4

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