What is factor 8x^6-27y^9 ?

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

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factor 8x^6-27y^9

factor

8 x^{6} - 27 y^{9}

(2 x^{2} - 3 y^{3}) (4 x^{4} + 6 x^{2} y^{3} + 9 y^{6})

Solution steps

8 x^{6} - 27 y^{9}

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(2 x^{2})^{2} + 2 x^{2} \cdot 3 y^{3} + (3 y^{3})^{2} : 4 x^{4} + 6 x^{2} y^{3} + 9 y^{6}

= (2 x^{2} - 3 y^{3}) (4 x^{4} + 6 x^{2} y^{3} + 9 y^{6})

\frac{2 x + 1}{x + 1} \leq 2

x^{2} - 6 x + 2 = 0

- \frac{5.98 E 16}{( 6.77 \cdot 1 0 ^{6} ) ^{3}}

y^{2} = 2 + y

8192 - 27

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