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

The solution to factor (y-3)^3-64y^3 is -9(y+1)(7y^2-6y+3)

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

factor

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

- 9 (y + 1) (7 y^{2} - 6 y + 3)

Solution steps

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

Rewrite

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

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

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Factor

- 3 y - 3 : - 3 (y + 1)

= (- 3 (y + 1)) (16 y^{2} + 4 y (y - 3) + (y - 3)^{2})

Factor

16 y^{2} + 4 y (y - 3) + (y - 3)^{2} : 3 (7 y^{2} - 6 y + 3)

= 3 (- 3 (y + 1)) (7 y^{2} - 6 y + 3)

Refine

= - 9 (y + 1) (7 y^{2} - 6 y + 3)

(sin (3 x))^{2}

\frac{( f ( x + h ) - f ( x ) )}{h}

g^{2} + 2 g n y + n^{2} y^{2}

1 - cos^{3} (A)

λ (- λ^{2} + 3 λ + 6 - 10)

What is factor (y-3)^3-64y^3 ?
The solution to factor (y-3)^3-64y^3 is -9(y+1)(7y^2-6y+3)