What is factor sin^6(θ)+cos^6(θ) ?

The solution to factor sin^6(θ)+cos^6(θ) is (sin^2(θ)+cos^2(θ))(sin^4(θ)-sin^2(θ)cos^2(θ)+cos^4(θ))

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factor sin^6(θ)+cos^6(θ)

factor

sin^{6} (θ) + cos^{6} (θ)

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

Solution steps

sin^{6} (θ) + cos^{6} (θ)

Rewrite

sin^{6} (θ) + cos^{6} (θ)

(sin^{2} (θ))^{3} + (cos^{2} (θ))^{3}

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

Apply Sum of Cubes Formula:

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

(sin^{2} (θ))^{3} + (cos^{2} (θ))^{3} = (sin^{2} (θ) + cos^{2} (θ)) (sin^{4} (θ) - sin^{2} (θ) cos^{2} (θ) + cos^{4} (θ))

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

\frac{x - 10}{x ^{2} - 100}

\cdot (\cdot + 4)

2^{1} \cdot 2^{n} - 2^{n}

4 m^{3} n + 4 m^{2} p + 3 pq + 3 n q m

x^{2} + 18 x + 49

What is factor sin^6(θ)+cos^6(θ) ?
The solution to factor sin^6(θ)+cos^6(θ) is (sin^2(θ)+cos^2(θ))(sin^4(θ)-sin^2(θ)cos^2(θ)+cos^4(θ))