What is factor (2x+y)^3-27 ?

The solution to factor (2x+y)^3-27 is (2x+y-3)((2x+y)^2+3(2x+y)+9)

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factor (2x+y)^3-27

factor

(2 x + y)^{3} - 27

(2 x + y - 3) ((2 x + y)^{2} + 3 (2 x + y) + 9)

Solution steps

(2 x + y)^{3} - 27

Rewrite

27

3^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

2 (17) - 102 + 32 (17)

2 cos^{2} (x) - 1 - cos (x)

(15 + 7)^{3} (15 - 7)^{3}

\frac{x ^{2} - 5 x + 6}{2 x + 6}

\frac{10 + 2 5}{2}

What is factor (2x+y)^3-27 ?
The solution to factor (2x+y)^3-27 is (2x+y-3)((2x+y)^2+3(2x+y)+9)