What is expand (rcos(x)-rsin(x))^2 ?

The solution to expand (rcos(x)-rsin(x))^2 is -r^2sin(2x)+r^2

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expand (rcos(x)-rsin(x))^2

expand

(r cos (x) - r sin (x))^{2}

- r^{2} sin (2 x) + r^{2}

Solution steps

(r cos (x) - r sin (x))^{2}

Apply Perfect Square Formula:

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

(r cos (x) - r sin (x))^{2} = (r cos (x))^{2} - 2 r cos (x) r sin (x) + (r sin (x))^{2}

= (r cos (x))^{2} - 2 r cos (x) r sin (x) + (r sin (x))^{2}

Simplify

(r cos (x))^{2} - 2 r cos (x) r sin (x) + (r sin (x))^{2} : r^{2} (- sin (2 x) + 1)

= r^{2} (- sin (2 x) + 1)

Apply the distributive law:

a (b + c) = ab + a c

r^{2} (- sin (2 x) + 1) = r^{2} (- sin (2 x)) + r^{2} \cdot 1

= r^{2} (- sin (2 x)) + r^{2} \cdot 1

Simplify

r^{2} (- sin (2 x)) + r^{2} \cdot 1 : - r^{2} sin (2 x) + r^{2}

= - r^{2} sin (2 x) + r^{2}

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

\frac{( 3 - s )}{( s ^{2} - 2 s + 2 )}

\frac{4 s}{( x + 1 ) ( x - 4 )}

(x + \frac{1}{4}) (x^{2} - 5 x)

(- (a) + a^{2} - 4 c)^{2}

What is expand (rcos(x)-rsin(x))^2 ?
The solution to expand (rcos(x)-rsin(x))^2 is -r^2sin(2x)+r^2