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

The solution to expand (4sin(x)+4cos(x))^2 is 16sin(2x)+16

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expand (4sin(x)+4cos(x))^2

expand

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

16 sin (2 x) + 16

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(4 sin (x))^{2} + 2 \cdot 4 sin (x) \cdot 4 cos (x) + (4 cos (x))^{2} : 16 (sin (2 x) + 1)

= 16 (sin (2 x) + 1)

Apply the distributive law:

a (b + c) = ab + a c

16 (sin (2 x) + 1) = 16 sin (2 x) + 16 \cdot 1

= 16 sin (2 x) + 16 \cdot 1

Multiply the numbers:

16 \cdot 1 = 16

= 16 sin (2 x) + 16

(a + ib)^{2}

(x - 3) (x + 3)

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

\frac{( k + 1 ) ^{2} ( k + 2 ) ^{2}}{4}

\frac{6}{2} (1 + 2)

What is expand (4sin(x)+4cos(x))^2 ?
The solution to expand (4sin(x)+4cos(x))^2 is 16sin(2x)+16