Simplify the following expression:
\((2x - 3y)^3 - 18xy(2x - 3y)\)
\(8x^3 - 27y^3 - 36x^2y - 54xy^2\)
\(8x^3 - 72x^2y + 108xy^2 - 27y^3\)
\(8x^3 - 27y^3\)
\(8x^3 + 108xy^2 - 72x^2y\)
Solve the following equation.
where θ is an acute angle.
Solve the following equation.
\(2\sqrt{3}\sin^{2}\theta+\cos\theta-\sqrt{3}=0\), where θ is an acute angle.
Using algebraic identities, simplify the following expression.
\(\dfrac{x^{4}+x^{2}+1}{x^{2}+x+1}\)
\((x^{2}-2x+1)\)
\((x^{2}+x+1)\)
\((x^{2}+2x+1)\)
\((x^{2}-x+1)\)
If a + b = p, ab = q, then (a4 + b4) is equal to:
p4 − 2p2q2 + q2
p4 − 4p2q2 + 2q2
p4 − 4p2q + q2
p4 − 4p2q + 2q2
Solve the following equation and find the value of θ.
3 cotθ + tanθ - 2\(\sqrt{3}\) = 0, 0° < θ < 90°