What is factor (x+2y)^3+1 ?

The solution to factor (x+2y)^3+1 is (x+2y+1)((x+2y)^2-x-2y+1)

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factor (x+2y)^3+1

factor

(x + 2 y)^{3} + 1

(x + 2 y + 1) ((x + 2 y)^{2} - x - 2 y + 1)

Solution steps

(x + 2 y)^{3} + 1

Rewrite

1

1^{3}

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

Apply Sum of Cubes Formula:

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

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

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

Refine

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

x^{3} - 6 x - 5 x + 30

x (2 y)

4 x^{2} a + 3 y + 12 a x + y x

(sin (2 x))^{4}

cos (f (t))

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