What is factor q^6-64 ?

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

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factor q^6-64

factor

q^{6} - 64

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

Solution steps

q^{6} - 64

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Factor

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

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

Factor

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

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

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

x^{2} + a x + b x + ab

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

5^{2} + 2^{2} = x^{2}

3 w^{2} - 11 w - 42

3 x^{2} + 24 x + 56 = 0

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