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

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

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simplify (sqrt(2)sin(x)+2cos(x))^2

simplify

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

2 sin^{2} (x) + 42 cos (x) sin (x) + 4 cos^{2} (x)

Solution steps

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

Apply Perfect Square Formula:

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

(2 sin (x) + 2 cos (x))^{2} = (2 sin (x))^{2} + 22 sin (x) \cdot 2 cos (x) + (2 cos (x))^{2}

= (2 sin (x))^{2} + 22 sin (x) \cdot 2 cos (x) + (2 cos (x))^{2}

(2 sin (x))^{2} = 2 sin^{2} (x)

22 sin (x) \cdot 2 cos (x) = 42 cos (x) sin (x)

(2 cos (x))^{2} = 4 cos^{2} (x)

= 2 sin^{2} (x) + 42 cos (x) sin (x) + 4 cos^{2} (x)

(2 + 2)^{4}

(6 e^{x} - 7) (e^{x} + 5)

(7 + 8) \cdot (63)

(1 + i) (a - bi) (3 + i)

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

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