What is factor sin^6(x)-cos^6(x) ?

The solution to factor sin^6(x)-cos^6(x) is (sin^3(x)+cos^3(x))(sin^3(x)-cos^3(x))

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factor sin^6(x)-cos^6(x)

factor

sin^{6} (x) - cos^{6} (x)

(sin^{3} (x) + cos^{3} (x)) (sin^{3} (x) - cos^{3} (x))

Solution steps

sin^{6} (x) - cos^{6} (x)

sin^{6} (x) = (sin^{3} (x))^{2}

cos^{6} (x) = (cos^{3} (x))^{2}

= (sin^{3} (x))^{2} - (cos^{3} (x))^{2}

Apply Difference of Two Squares Formula:

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

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

= (sin^{3} (x) + cos^{3} (x)) (sin^{3} (x) - cos^{3} (x))

\frac{cos ^{2} ( x )}{2} - \frac{sin ^{2} ( x )}{2}

(5 - 2 x)^{3}

3 x^{2} - 10 x y + 3 y^{2}

x^{3} - 9 y^{3} + (x + y)^{3}

12 x^{3} - 5 x^{2} + 1

What is factor sin^6(x)-cos^6(x) ?
The solution to factor sin^6(x)-cos^6(x) is (sin^3(x)+cos^3(x))(sin^3(x)-cos^3(x))