Algebra Examples

$2 x^{2} + 2 y^{2} - 5 x - 4 y + 5 x y + 2$

Step 1

Regroup terms.

$- 5 x + 5 x y + 2 x^{2} + 2 y^{2} - 4 y + 2$

Step 2

Factor $- 5 x$ out of $- 5 x + 5 x y$ .

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Step 2.1

Reorder $- 5 x$ and $5 x y$ .

$5 x y - 5 x + 2 x^{2} + 2 y^{2} - 4 y + 2$

Step 2.2

Factor $- 5 x$ out of $5 x y$ .

$- 5 x (- 1 y) - 5 x + 2 x^{2} + 2 y^{2} - 4 y + 2$

Step 2.3

Factor $- 5 x$ out of $- 5 x$ .

$- 5 x (- 1 y) - 5 x (1) + 2 x^{2} + 2 y^{2} - 4 y + 2$

Step 2.4

Factor $- 5 x$ out of $- 5 x (- 1 y) - 5 x (1)$ .

$- 5 x (- 1 y + 1) + 2 x^{2} + 2 y^{2} - 4 y + 2$

Step 3

Rewrite $- 1 y$ as $- y$ .

$- 5 x (- y + 1) + 2 x^{2} + 2 y^{2} - 4 y + 2$

Step 4

Factor $2$ out of $2 x^{2} + 2 y^{2} - 4 y + 2$ .

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Step 4.1

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

$- 5 x (- y + 1) + 2 (x^{2}) + 2 y^{2} - 4 y + 2$

Step 4.2

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

$- 5 x (- y + 1) + 2 (x^{2}) + 2 (y^{2}) - 4 y + 2$

Step 4.3

Factor $2$ out of $- 4 y$ .

$- 5 x (- y + 1) + 2 (x^{2}) + 2 (y^{2}) + 2 (- 2 y) + 2$

Step 4.4

Factor $2$ out of $2$ .

$- 5 x (- y + 1) + 2 (x^{2}) + 2 (y^{2}) + 2 (- 2 y) + 2 (1)$

Step 4.5

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

$- 5 x (- y + 1) + 2 (x^{2} + y^{2}) + 2 (- 2 y) + 2 (1)$

Step 4.6

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

$- 5 x (- y + 1) + 2 (x^{2} + y^{2} - 2 y) + 2 (1)$

Step 4.7

Factor $2$ out of $2 (x^{2} + y^{2} - 2 y) + 2 (1)$ .

$- 5 x (- y + 1) + 2 (x^{2} + y^{2} - 2 y + 1)$

Step 5

Factor $- 1$ out of $- 5 x (- y + 1) + 2 (x^{2} + y^{2} - 2 y + 1)$ .

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Step 5.1

Reorder $- 5 x (- y + 1)$ and $2 (x^{2} + y^{2} - 2 y + 1)$ .

$2 (x^{2} + y^{2} - 2 y + 1) - 5 x (- y + 1)$

Step 5.2

Factor $- 1$ out of $2 (x^{2} + y^{2} - 2 y + 1)$ .

$- (- 2 (x^{2} + y^{2} - 2 y + 1)) - 5 x (- y + 1)$

Step 5.3

Factor $- 1$ out of $- 5 x (- y + 1)$ .

$- (- 2 (x^{2} + y^{2} - 2 y + 1)) - (5 x (- y + 1))$

Step 5.4

Factor $- 1$ out of $- (- 2 (x^{2} + y^{2} - 2 y + 1)) - (5 x (- y + 1))$ .

$- (- 2 (x^{2} + y^{2} - 2 y + 1) + 5 x (- y + 1))$

Step 6

Apply the distributive property.

$- (- 2 x^{2} - 2 y^{2} - 2 (- 2 y) - 2 \cdot 1 + 5 x (- y + 1))$

Step 7

Simplify.

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Step 7.1

Multiply $- 2$ by $- 2$ .

$- (- 2 x^{2} - 2 y^{2} + 4 y - 2 \cdot 1 + 5 x (- y + 1))$

Step 7.2

Multiply $- 2$ by $1$ .

$- (- 2 x^{2} - 2 y^{2} + 4 y - 2 + 5 x (- y + 1))$

Step 8

Apply the distributive property.

$- (- 2 x^{2} - 2 y^{2} + 4 y - 2 + 5 x (- y) + 5 x \cdot 1)$

Step 9

Rewrite using the commutative property of multiplication.

$- (- 2 x^{2} - 2 y^{2} + 4 y - 2 + 5 \cdot - 1 x y + 5 x \cdot 1)$

Step 10

Multiply $5$ by $1$ .

$- (- 2 x^{2} - 2 y^{2} + 4 y - 2 + 5 \cdot - 1 x y + 5 x)$

Step 11

Multiply $5$ by $- 1$ .

$- (- 2 x^{2} - 2 y^{2} + 4 y - 2 - 5 x y + 5 x)$