What is factor u^6-64 ?

The solution to factor u^6-64 is (u+2)(u-2)(u^2+2u+4)(u^2-2u+4)

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factor u^6-64

factor

u^{6} - 64

(u + 2) (u - 2) (u^{2} + 2 u + 4) (u^{2} - 2 u + 4)

Solution steps

u^{6} - 64

Apply exponent rules

= (u^{2})^{3} - 4^{3}

Apply Difference of Cubes Formula:

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

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

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

Factor

u^{2} - 4 : (u + 2) (u - 2)

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

Factor

u^{4} + 4 u^{2} + 4^{2} : (u^{2} + 4 + 2 u) (u^{2} + 4 - 2 u)

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

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

\frac{22}{12}

72 + 32 + 2

- 14 \div 2

\frac{x ^{2} + 6 x + 9}{x ^{2} + 2 x - 3}

(3 x - 2)^{4}

What is factor u^6-64 ?
The solution to factor u^6-64 is (u+2)(u-2)(u^2+2u+4)(u^2-2u+4)