What is factor 125x^6-8 ?

The solution to factor 125x^6-8 is (5x^2-2)(25x^4+10x^2+4)

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factor 125x^6-8

factor

125 x^{6} - 8

(5 x^{2} - 2) (25 x^{4} + 10 x^{2} + 4)

Solution steps

125 x^{6} - 8

Apply exponent rules

= (5 x^{2})^{3} - 2^{3}

Apply Difference of Cubes Formula:

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

(5 x^{2})^{3} - 2^{3} = (5 x^{2} - 2) (5^{2} x^{4} + 2 \cdot 5 x^{2} + 2^{2})

= (5 x^{2} - 2) (5^{2} x^{4} + 2 \cdot 5 x^{2} + 2^{2})

Simplify

(5 x^{2} - 2) (5^{2} x^{4} + 2 \cdot 5 x^{2} + 2^{2}) : (5 x^{2} - 2) (25 x^{4} + 10 x^{2} + 4)

= (5 x^{2} - 2) (25 x^{4} + 10 x^{2} + 4)

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

(3 x + 1) (x + 2) (x - 3)

- 9 \times 7

(a - 3)^{5}

(- 1 - i)^{16}

What is factor 125x^6-8 ?
The solution to factor 125x^6-8 is (5x^2-2)(25x^4+10x^2+4)