What is expand (-sin(2t)+3sin(t))^2 ?

The solution to expand (-sin(2t)+3sin(t))^2 is sin^2(2t)-6sin(2t)sin(t)+9sin^2(t)

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expand (-sin(2t)+3sin(t))^2

expand

(- sin (2 t) + 3 sin (t))^{2}

sin^{2} (2 t) - 6 sin (2 t) sin (t) + 9 sin^{2} (t)

Solution steps

(- sin (2 t) + 3 sin (t))^{2}

Apply Perfect Square Formula:

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

(- sin (2 t) + 3 sin (t))^{2} = (- sin (2 t))^{2} + 2 (- sin (2 t)) \cdot 3 sin (t) + (3 sin (t))^{2}

= (- sin (2 t))^{2} + 2 (- sin (2 t)) \cdot 3 sin (t) + (3 sin (t))^{2}

Simplify

(- sin (2 t))^{2} + 2 (- sin (2 t)) \cdot 3 sin (t) + (3 sin (t))^{2} : sin^{2} (2 t) - 6 sin (2 t) sin (t) + 9 sin^{2} (t)

= sin^{2} (2 t) - 6 sin (2 t) sin (t) + 9 sin^{2} (t)

(2 x + \frac{k}{x})^{8}

\frac{1 - e ^{- s}}{s ( s ^{2} + 3 s + 2 )}

(x + 3 - 2 i) (x + 3 + 2 i)

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

What is expand (-sin(2t)+3sin(t))^2 ?
The solution to expand (-sin(2t)+3sin(t))^2 is sin^2(2t)-6sin(2t)sin(t)+9sin^2(t)