What is factor (y-5)^3-64y^3 ?

The solution to factor (y-5)^3-64y^3 is (-3y-5)(21y^2-30y+25)

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factor (y-5)^3-64y^3

factor

(y - 5)^{3} - 64 y^{3}

(- 3 y - 5) (21 y^{2} - 30 y + 25)

Solution steps

(y - 5)^{3} - 64 y^{3}

Rewrite

(y - 5)^{3} - 64 y^{3}

(y - 5)^{3} - (4 y)^{3}

= (y - 5)^{3} - (4 y)^{3}

Apply Difference of Cubes Formula:

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

(y - 5)^{3} - (4 y)^{3} = ((y - 5) - 4 y) ((y - 5)^{2} + 4 y (y - 5) + 4^{2} y^{2})

= ((y - 5) - 4 y) (4^{2} y^{2} + 4 y (y - 5) + (y - 5)^{2})

Refine

= (- 3 y - 5) (16 y^{2} + 4 y (y - 5) + (y - 5)^{2})

Expand

16 y^{2} + 4 y (y - 5) + (y - 5)^{2} : 21 y^{2} - 30 y + 25

= (- 3 y - 5) (21 y^{2} - 30 y + 25)

\frac{81 π + 648 3}{2}

- l^{6} - 8 l

(u)^{2}

- 45 w z + (- 5 z)

x^{2} z^{2} + x yz + x z v + y v

What is factor (y-5)^3-64y^3 ?
The solution to factor (y-5)^3-64y^3 is (-3y-5)(21y^2-30y+25)