What is factor 27x^6-125y^6 ?

The solution to factor 27x^6-125y^6 is (3x^2-5y^2)(9x^4+15x^2y^2+25y^4)

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factor 27x^6-125y^6

factor

27 x^{6} - 125 y^{6}

(3 x^{2} - 5 y^{2}) (9 x^{4} + 15 x^{2} y^{2} + 25 y^{4})

Solution steps

27 x^{6} - 125 y^{6}

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(3 x^{2})^{2} + 3 x^{2} \cdot 5 y^{2} + (5 y^{2})^{2} : 9 x^{4} + 15 x^{2} y^{2} + 25 y^{4}

= (3 x^{2} - 5 y^{2}) (9 x^{4} + 15 x^{2} y^{2} + 25 y^{4})

2 v^{2} - 47 = 61

6 x + 7 = 5 x + 13

8 (3 n + 5) = - 32

x^{2} = 2 (6!) (3 x - 6!) - 7 (6!)^{2}

3 x^{4} - 24 x^{2} + 48

What is factor 27x^6-125y^6 ?
The solution to factor 27x^6-125y^6 is (3x^2-5y^2)(9x^4+15x^2y^2+25y^4)