What is factor x^6-(x+2)^3 ?

The solution to factor x^6-(x+2)^3 is (x+1)(x-2)(x^4+x^3+3x^2+4x+4)

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factor x^6-(x+2)^3

factor

x^{6} - (x + 2)^{3}

(x + 1) (x - 2) (x^{4} + x^{3} + 3 x^{2} + 4 x + 4)

Solution steps

x^{6} - (x + 2)^{3}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

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

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

Apply Difference of Cubes Formula:

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

(x^{2})^{3} - (x + 2)^{3} = (x^{2} - (x + 2)) (x^{4} + x^{2} (x + 2) + (x + 2)^{2})

= (x^{2} - (x + 2)) (x^{4} + x^{2} (x + 2) + (x + 2)^{2})

Refine

= (x^{2} - x - 2) (x^{4} + x^{2} (x + 2) + (x + 2)^{2})

Factor

x^{2} - x - 2 : (x + 1) (x - 2)

= (x + 1) (x - 2) (x^{4} + x^{2} (x + 2) + (x + 2)^{2})

Expand

x^{4} + x^{2} (x + 2) + (x + 2)^{2} : x^{4} + x^{3} + 3 x^{2} + 4 x + 4

= (x + 1) (x - 2) (x^{4} + x^{3} + 3 x^{2} + 4 x + 4)

x^{6} - (x - 2)^{3}

sin (x^{5}) + ln (x^{2} + x)

8 x^{9} - 125 y^{6} z^{9}

e^{2 x} - 8 e^{x} + 15

[1 - sin (a)] [1 + sin (a)]

What is factor x^6-(x+2)^3 ?
The solution to factor x^6-(x+2)^3 is (x+1)(x-2)(x^4+x^3+3x^2+4x+4)