What is factor x^3y^6-64 ?

The solution to factor x^3y^6-64 is (xy^2-4)(x^2y^4+4xy^2+16)

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factor x^3y^6-64

factor

x^{3} y^{6} - 64

(x y^{2} - 4) (x^{2} y^{4} + 4 x y^{2} + 16)

Solution steps

x^{3} y^{6} - 64

Apply exponent rules

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

Apply Difference of Cubes Formula:

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

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

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

Simplify

(x y^{2})^{2} + 4 x y^{2} + 4^{2} : x^{2} y^{4} + 4 x y^{2} + 16

= (x y^{2} - 4) (x^{2} y^{4} + 4 x y^{2} + 16)

\frac{( 2 x ) ^{- 4}}{x ^{- 1} \cdot x}

\frac{x ^{15} + y ^{15}}{x ^{3} + y ^{3}}

(x^{3} - 2 x^{2} + 3 x - 1) (2 x + 3)

\frac{lo g _{10} ( 7 )}{lo g _{10} ( 5 )}

- \frac{2}{2} + 1

What is factor x^3y^6-64 ?
The solution to factor x^3y^6-64 is (xy^2-4)(x^2y^4+4xy^2+16)