What is factor 343a^3b^3-512x^3y^6 ?

The solution to factor 343a^3b^3-512x^3y^6 is (7ab-8xy^2)(49a^2b^2+56abxy^2+64x^2y^4)

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factor 343a^3b^3-512x^3y^6

factor

343 a^{3} b^{3} - 512 x^{3} y^{6}

(7 ab - 8 x y^{2}) (49 a^{2} b^{2} + 56 ab x y^{2} + 64 x^{2} y^{4})

Solution steps

343 a^{3} b^{3} - 512 x^{3} y^{6}

Rewrite

343 a^{3} b^{3}

(7 ab)^{3}

Rewrite

512 x^{3} y^{6}

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

= (7 ab)^{3} - (2^{3} x y^{2})^{3}

Apply Difference of Cubes Formula:

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

(7 ab)^{3} - (2^{3} x y^{2})^{3} = (7 ab - 2^{3} x y^{2}) ((7 ab)^{2} + 2^{3} x y^{2} 7 ab + (2^{3} x y^{2})^{2})

= (7 ab - 2^{3} x y^{2}) ((2^{3} x y^{2})^{2} + 2^{3} x y^{2} 7 ab + (7 ab)^{2})

Simplify

(7 ab - 2^{3} x y^{2}) ((7 ab)^{2} + 2^{3} x y^{2} \cdot 7 ab + (2^{3} x y^{2})^{2}) : (7 ab - 8 x y^{2}) (49 a^{2} b^{2} + 56 ab x y^{2} + 64 x^{2} y^{4})

= (7 ab - 8 x y^{2}) (49 a^{2} b^{2} + 56 ab x y^{2} + 64 x^{2} y^{4})

t y - x z - t z + x y

(x)^{4} + 3 (x)^{3} - 2

8 a^{2} - 6 a^{2}

3 x 2 - 5 x + 8

x^{2 - x - 264}

What is factor 343a^3b^3-512x^3y^6 ?
The solution to factor 343a^3b^3-512x^3y^6 is (7ab-8xy^2)(49a^2b^2+56abxy^2+64x^2y^4)