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

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

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factor x^6-64y^6

factor

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

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

Solution steps

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

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

64 y^{6} = (8 y^{3})^{2}

= (x^{3})^{2} - (8 y^{3})^{2}

Apply Difference of Two Squares Formula:

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

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

= (x^{3} + 8 y^{3}) (x^{3} - 8 y^{3})

Factor

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

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

Factor

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

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

x^{n} x^{m}

4 \cdot (- 16)

49 + 3 \cdot (12 - 7)

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

\frac{6}{5} \cdot \frac{4}{3}

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