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

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

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factor 64x^6-y^6

factor

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

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

Solution steps

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

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

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

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

Apply Difference of Two Squares Formula:

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

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

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

Factor

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

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

Factor

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

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

2^{\frac{1}{2}} \cdot 3 2^{\frac{1}{2}}

90 \cdot \frac{1}{3}

5 x^{2} + 1 = 2 x

6 x - x^{2} - x^{3}

(x - 2)^{2} > (x + 2) (x - 2) + 8

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