What is factor (2x+y)^3-8 ?

The solution to factor (2x+y)^3-8 is (2x+y-2)((2x+y)^2+2(2x+y)+4)

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factor (2x+y)^3-8

factor

(2 x + y)^{3} - 8

(2 x + y - 2) ((2 x + y)^{2} + 2 (2 x + y) + 4)

Solution steps

(2 x + y)^{3} - 8

Rewrite

8

2^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

2 (x + y)^{2} + 5 (x + y) + 3

(x + 2) (x + 2)

64 x^{3} y^{9} - 125 z^{3} w^{6}

x^{5} - 2 x^{- 2}

3 a x + 3 a y - 2 b x - 2 b y

What is factor (2x+y)^3-8 ?
The solution to factor (2x+y)^3-8 is (2x+y-2)((2x+y)^2+2(2x+y)+4)