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

The solution to factor (2x-y)^3+(3x+y)^3 is 5x(7x^2+3xy+3y^2)

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

factor

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

5 x (7 x^{2} + 3 x y + 3 y^{2})

Solution steps

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

Apply Sum of Cubes Formula:

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

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

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

Refine

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

Expand

(2 x - y)^{2} - (2 x - y) (3 x + y) + (3 x + y)^{2} : 7 x^{2} + 3 x y + 3 y^{2}

= 5 x (7 x^{2} + 3 x y + 3 y^{2})

8 5 + 105

a^{x} - a^{x + 2}

\frac{x - 1}{1 - x ^{2}}

[- 10.1]

\frac{164 82 - 2}{243}

What is factor (2x-y)^3+(3x+y)^3 ?
The solution to factor (2x-y)^3+(3x+y)^3 is 5x(7x^2+3xy+3y^2)