What is factor sin^3(θ)+cos^3(θ) ?

The solution to factor sin^3(θ)+cos^3(θ) is (sin(θ)+cos(θ))(sin^2(θ)-sin(θ)cos(θ)+cos^2(θ))

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factor sin^3(θ)+cos^3(θ)

factor

sin^{3} (θ) + cos^{3} (θ)

(sin (θ) + cos (θ)) (sin^{2} (θ) - sin (θ) cos (θ) + cos^{2} (θ))

Solution steps

sin^{3} (θ) + cos^{3} (θ)

Apply Sum of Cubes Formula:

x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})

sin^{3} (θ) + cos^{3} (θ) = (sin (θ) + cos (θ)) (sin^{2} (θ) - sin (θ) cos (θ) + cos^{2} (θ))

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

2 (ab)

4 x^{2} - 2 x y + 9 yz - 18 x z

(x + y)^{2} - 10 (x + y) + 25

8 a^{6} b^{3} + 125 c^{3}

(x + 5) (x + 5)

What is factor sin^3(θ)+cos^3(θ) ?
The solution to factor sin^3(θ)+cos^3(θ) is (sin(θ)+cos(θ))(sin^2(θ)-sin(θ)cos(θ)+cos^2(θ))