What is factor x^{12}y^6+27z^3 ?

The solution to factor x^{12}y^6+27z^3 is (x^4y^2+3z)(x^8y^4-3x^4y^2z+9z^2)

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factor x^{12}y^6+27z^3

factor

x^{12} y^{6} + 27 z^{3}

(x^{4} y^{2} + 3 z) (x^{8} y^{4} - 3 x^{4} y^{2} z + 9 z^{2})

Solution steps

x^{12} y^{6} + 27 z^{3}

Rewrite

x^{12} y^{6}

(x^{2} y)^{6}

Rewrite

27 z^{3}

(3 z)^{3}

= (x^{2} y)^{6} + (3 z)^{3}

Apply exponent rule:

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

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

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

Apply Sum of Cubes Formula:

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

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

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

Simplify

((x^{2} y)^{2} + 3 z) ((x^{2} y)^{4} - 3 z (x^{2} y)^{2} + (3 z)^{2}) : (x^{4} y^{2} + 3 z) (x^{8} y^{4} - 3 x^{4} y^{2} z + 9 z^{2})

= (x^{4} y^{2} + 3 z) (x^{8} y^{4} - 3 x^{4} y^{2} z + 9 z^{2})

(2 a^{2} - g) + (a + 3)

sin^{-} (1) (2 x)

m^{2 + 10 m}

\frac{x - 5}{10 - 2 x}

a x - a + b x - b - c x + c

What is factor x^{12}y^6+27z^3 ?
The solution to factor x^{12}y^6+27z^3 is (x^4y^2+3z)(x^8y^4-3x^4y^2z+9z^2)