What is expand (rcos^2(θ)+rsin^2(θ))^2 ?

The solution to expand (rcos^2(θ)+rsin^2(θ))^2 is r^2cos^4(θ)+2r^2cos^2(θ)sin^2(θ)+r^2sin^4(θ)

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expand (rcos^2(θ)+rsin^2(θ))^2

expand

(r cos^{2} (θ) + r sin^{2} (θ))^{2}

r^{2} cos^{4} (θ) + 2 r^{2} cos^{2} (θ) sin^{2} (θ) + r^{2} sin^{4} (θ)

Solution steps

(r cos^{2} (θ) + r sin^{2} (θ))^{2}

Apply Perfect Square Formula:

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

(r cos^{2} (θ) + r sin^{2} (θ))^{2} = (r cos^{2} (θ))^{2} + 2 r cos^{2} (θ) r sin^{2} (θ) + (r sin^{2} (θ))^{2}

= (r cos^{2} (θ))^{2} + 2 r cos^{2} (θ) r sin^{2} (θ) + (r sin^{2} (θ))^{2}

Simplify

(r cos^{2} (θ))^{2} + 2 r cos^{2} (θ) r sin^{2} (θ) + (r sin^{2} (θ))^{2} : r^{2} cos^{4} (θ) + 2 r^{2} cos^{2} (θ) sin^{2} (θ) + r^{2} sin^{4} (θ)

= r^{2} cos^{4} (θ) + 2 r^{2} cos^{2} (θ) sin^{2} (θ) + r^{2} sin^{4} (θ)

(1 + e^{- 3 t} + e^{2 t}) \cdot (e^{t} + 2 e^{2 t} - e^{- t})

\frac{( x - 4 )}{( x - 2 ) ^{2}}

\frac{10 z}{( z - 1 ) ( z + 2 )}

\frac{100 ( x + 55 )}{x + 550}

\frac{n ^{2}}{( 2 i d x + 2 i ^{2} d ^{2} ) ( s + x + i d )}

What is expand (rcos^2(θ)+rsin^2(θ))^2 ?
The solution to expand (rcos^2(θ)+rsin^2(θ))^2 is r^2cos^4(θ)+2r^2cos^2(θ)sin^2(θ)+r^2sin^4(θ)