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

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

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

expand

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

4 sin (2 x) + 4

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

= 4 (sin (2 x) + 1)

Apply the distributive law:

a (b + c) = ab + a c

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

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

Multiply the numbers:

4 \cdot 1 = 4

= 4 sin (2 x) + 4

\frac{2 x ( - x ^{2} - 3 )}{25}

\frac{d ^{2}}{d r d s} ((r (s)) (\frac{1}{r ( s )} + \frac{1}{s}))

(x^{3})^{2}

x^{s i n (π)} (cos (π) ln (π) + \frac{sin ( π )}{π})

sin (x) (sec (x) + cot (x))

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