Algebra Examples

$x^{3} + y^{3} + 2 x^{2} - 2 x y + 2 y^{2}$

Step 1

Regroup terms.

$x^{3} + y^{3} + 2 x^{2} - 2 x y + 2 y^{2}$

Step 2

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = x$ and $b = y$ .

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

Step 3

Factor $2$ out of $2 x^{2} - 2 x y + 2 y^{2}$ .

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Step 3.1

Factor $2$ out of $2 x^{2}$ .

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

Step 3.2

Factor $2$ out of $- 2 x y$ .

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

Step 3.3

Factor $2$ out of $2 y^{2}$ .

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

Step 3.4

Factor $2$ out of $2 (x^{2}) + 2 (- x y)$ .

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

Step 3.5

Factor $2$ out of $2 (x^{2} - x y) + 2 (y^{2})$ .

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

Step 4

Factor $x^{2} - x y + y^{2}$ out of $(x + y) (x^{2} - x y + y^{2}) + 2 (x^{2} - x y + y^{2})$ .

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Step 4.1

Factor $x^{2} - x y + y^{2}$ out of $(x + y) (x^{2} - x y + y^{2})$ .

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

Step 4.2

Factor $x^{2} - x y + y^{2}$ out of $2 (x^{2} - x y + y^{2})$ .

$(x^{2} - x y + y^{2}) (x + y) + (x^{2} - x y + y^{2}) \cdot 2$

Step 4.3

Factor $x^{2} - x y + y^{2}$ out of $(x^{2} - x y + y^{2}) (x + y) + (x^{2} - x y + y^{2}) \cdot 2$ .

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