What is factor sin^3(x)-cos^3(x) ?

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

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factor sin^3(x)-cos^3(x)

factor

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

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

Solution steps

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

Apply Difference of Cubes Formula:

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

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

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

[5.9]

8 ab - 2 a d - 12 b + 3 d

(a)^{3}

4 e^{2} + 7 e^{3} - 9 e^{4}

[- 5.5]

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