What is expand (2acos(t)-acos(2t))^2 ?

The solution to expand (2acos(t)-acos(2t))^2 is 4a^2cos^2(t)-4a^2cos(t)cos(2t)+a^2cos^2(2t)

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expand (2acos(t)-acos(2t))^2

expand

(2 a cos (t) - a cos (2 t))^{2}

4 a^{2} cos^{2} (t) - 4 a^{2} cos (t) cos (2 t) + a^{2} cos^{2} (2 t)

Solution steps

(2 a cos (t) - a cos (2 t))^{2}

Apply Perfect Square Formula:

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

(2 a cos (t) - a cos (2 t))^{2} = (2 a cos (t))^{2} - 2 \cdot 2 a cos (t) a cos (2 t) + (a cos (2 t))^{2}

= (2 a cos (t))^{2} - 2 \cdot 2 a cos (t) a cos (2 t) + (a cos (2 t))^{2}

Simplify

(2 a cos (t))^{2} - 2 \cdot 2 a cos (t) a cos (2 t) + (a cos (2 t))^{2} : 4 a^{2} cos^{2} (t) - 4 a^{2} cos (t) cos (2 t) + a^{2} cos^{2} (2 t)

= 4 a^{2} cos^{2} (t) - 4 a^{2} cos (t) cos (2 t) + a^{2} cos^{2} (2 t)

\frac{20}{49 ( x - 9.45 ) ^{2} + 3.004}

y^{3} e^{x} + \frac{( 1 + 4 y ^{2} e ^{x} ) d y}{d x}

(x - \frac{3}{x ^{2}})^{9}

\frac{x ( t ^{2} - 16 )}{cos ^{2} ( t ) + 1}

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

What is expand (2acos(t)-acos(2t))^2 ?
The solution to expand (2acos(t)-acos(2t))^2 is 4a^2cos^2(t)-4a^2cos(t)cos(2t)+a^2cos^2(2t)