What is factor (y+1)^3-27y^3 ?

The solution to factor (y+1)^3-27y^3 is (-2y+1)(13y^2+5y+1)

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factor (y+1)^3-27y^3

factor

(y + 1)^{3} - 27 y^{3}

(- 2 y + 1) (13 y^{2} + 5 y + 1)

Solution steps

(y + 1)^{3} - 27 y^{3}

Rewrite

(y + 1)^{3} - 27 y^{3}

(y + 1)^{3} - (3 y)^{3}

= (y + 1)^{3} - (3 y)^{3}

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Expand

9 y^{2} + 3 y (y + 1) + (y + 1)^{2} : 13 y^{2} + 5 y + 1

= (- 2 y + 1) (13 y^{2} + 5 y + 1)

C (11.7)

5 + (2 x + 3) 2 - (3 x + 2) (x + 1)

(4 x^{2})^{2} - 8 (4 x^{2}) - 105

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

m p + m q - 3 p - 3 q

What is factor (y+1)^3-27y^3 ?
The solution to factor (y+1)^3-27y^3 is (-2y+1)(13y^2+5y+1)