What is factor (x+y)^3-(2+3y)^3 ?

The solution to factor (x+y)^3-(2+3y)^3 is (-2y+x-2)(13y^2+5xy+14y+x^2+2x+4)

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factor (x+y)^3-(2+3y)^3

factor

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

(- 2 y + x - 2) (13 y^{2} + 5 x y + 14 y + x^{2} + 2 x + 4)

Solution steps

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Expand

(x + y)^{2} + (2 + 3 y) (x + y) + (2 + 3 y)^{2} : 13 y^{2} + 5 x y + 14 y + x^{2} + 2 x + 4

= (x - 2 y - 2) (x^{2} + 5 x y + 2 x + 13 y^{2} + 14 y + 4)

2 x^{2} - \frac{10}{3} x + \frac{4}{3} = 0

3 x^{2} - 11 x + 10

3 x^{2} - 8 x + 4

\frac{π}{3} + 4 π

What is factor (x+y)^3-(2+3y)^3 ?
The solution to factor (x+y)^3-(2+3y)^3 is (-2y+x-2)(13y^2+5xy+14y+x^2+2x+4)