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

Simplify

16 (- sin (2 x)) + 16 \cdot 1 : - 16 sin (2 x) + 16

= - 16 sin (2 x) + 16

(e^{y} + 1)^{2}

\frac{6 ( x + y ) + 5 - 6 x + 5}{y}

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

(32 + 1) (2 - 3)

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

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