What is factor 8x^9-125y^3z^6 ?

The solution to factor 8x^9-125y^3z^6 is (2x^3-5yz^2)(4x^6+10x^3yz^2+25y^2z^4)

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factor 8x^9-125y^3z^6

factor

8 x^{9} - 125 y^{3} z^{6}

(2 x^{3} - 5 y z^{2}) (4 x^{6} + 10 x^{3} y z^{2} + 25 y^{2} z^{4})

Solution steps

8 x^{9} - 125 y^{3} z^{6}

Rewrite

8 x^{9}

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

Rewrite

125 y^{3} z^{6}

(5 y z^{2})^{3}

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

Apply Difference of Cubes Formula:

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

(2 x^{3})^{3} - (5 y z^{2})^{3} = (2 x^{3} - 5 y z^{2}) ((2 x^{3})^{2} + 2 x^{3} 5 y z^{2} + (5 y z^{2})^{2})

= (2 x^{3} - 5 y z^{2}) ((2 x^{3})^{2} + 2 x^{3} 5 y z^{2} + (5 y z^{2})^{2})

Simplify

(2 x^{3} - 5 y z^{2}) ((2 x^{3})^{2} + 2 x^{3} \cdot 5 y z^{2} + (5 y z^{2})^{2}) : (2 x^{3} - 5 y z^{2}) (4 x^{6} + 10 x^{3} y z^{2} + 25 y^{2} z^{4})

= (2 x^{3} - 5 y z^{2}) (4 x^{6} + 10 x^{3} y z^{2} + 25 y^{2} z^{4})

8 \cdot 1 0^{6}

7 - 3 (6 c + 14) > 5 (1 - 2 c)

12 x^{2} - x - 1 = 0

9 x^{2} + 31 x + 12 \leq 0

x + 1 = 3 x + 1

What is factor 8x^9-125y^3z^6 ?
The solution to factor 8x^9-125y^3z^6 is (2x^3-5yz^2)(4x^6+10x^3yz^2+25y^2z^4)