Algebra Examples

$6 x^{2} - x y^{2} - 2 y^{2} + 17 x - 2 y + 12$

Step 1

Regroup terms.

$- x y^{2} + 17 x + 6 x^{2} - 2 y^{2} - 2 y + 12$

Step 2

Factor $- x$ out of $- x y^{2} + 17 x$ .

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Step 2.1

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

$- x (y^{2}) + 17 x + 6 x^{2} - 2 y^{2} - 2 y + 12$

Step 2.2

Factor $- x$ out of $17 x$ .

$- x (y^{2}) - x (- 17) + 6 x^{2} - 2 y^{2} - 2 y + 12$

Step 2.3

Factor $- x$ out of $- x (y^{2}) - x (- 17)$ .

$- x (y^{2} - 17) + 6 x^{2} - 2 y^{2} - 2 y + 12$

Step 3

Factor $2$ out of $6 x^{2} - 2 y^{2} - 2 y + 12$ .

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Step 3.1

Factor $2$ out of $6 x^{2}$ .

$- x (y^{2} - 17) + 2 (3 x^{2}) - 2 y^{2} - 2 y + 12$

Step 3.2

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

$- x (y^{2} - 17) + 2 (3 x^{2}) + 2 (- y^{2}) - 2 y + 12$

Step 3.3

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

$- x (y^{2} - 17) + 2 (3 x^{2}) + 2 (- y^{2}) + 2 (- y) + 12$

Step 3.4

Factor $2$ out of $12$ .

$- x (y^{2} - 17) + 2 (3 x^{2}) + 2 (- y^{2}) + 2 (- y) + 2 (6)$

Step 3.5

Factor $2$ out of $2 (3 x^{2}) + 2 (- y^{2})$ .

$- x (y^{2} - 17) + 2 (3 x^{2} - y^{2}) + 2 (- y) + 2 (6)$

Step 3.6

Factor $2$ out of $2 (3 x^{2} - y^{2}) + 2 (- y)$ .

$- x (y^{2} - 17) + 2 (3 x^{2} - y^{2} - y) + 2 (6)$

Step 3.7

Factor $2$ out of $2 (3 x^{2} - y^{2} - y) + 2 (6)$ .

$- x (y^{2} - 17) + 2 (3 x^{2} - y^{2} - y + 6)$

Step 4

Factor $- 1$ out of $- x (y^{2} - 17) + 2 (3 x^{2} - y^{2} - y + 6)$ .

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Step 4.1

Reorder $- x (y^{2} - 17)$ and $2 (3 x^{2} - y^{2} - y + 6)$ .

$2 (3 x^{2} - y^{2} - y + 6) - x (y^{2} - 17)$

Step 4.2

Factor $- 1$ out of $2 (3 x^{2} - y^{2} - y + 6)$ .

$- (- 2 (3 x^{2} - y^{2} - y + 6)) - x (y^{2} - 17)$

Step 4.3

Factor $- 1$ out of $- x (y^{2} - 17)$ .

$- (- 2 (3 x^{2} - y^{2} - y + 6)) - (x (y^{2} - 17))$

Step 4.4

Factor $- 1$ out of $- (- 2 (3 x^{2} - y^{2} - y + 6)) - (x (y^{2} - 17))$ .

$- (- 2 (3 x^{2} - y^{2} - y + 6) + x (y^{2} - 17))$

Step 5

Apply the distributive property.

$- (- 2 (3 x^{2}) - 2 (- y^{2}) - 2 (- y) - 2 \cdot 6 + x (y^{2} - 17))$

Step 6

Simplify.

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Step 6.1

Multiply $3$ by $- 2$ .

$- (- 6 x^{2} - 2 (- y^{2}) - 2 (- y) - 2 \cdot 6 + x (y^{2} - 17))$

Step 6.2

Multiply $- 1$ by $- 2$ .

$- (- 6 x^{2} + 2 y^{2} - 2 (- y) - 2 \cdot 6 + x (y^{2} - 17))$

Step 6.3

Multiply $- 1$ by $- 2$ .

$- (- 6 x^{2} + 2 y^{2} + 2 y - 2 \cdot 6 + x (y^{2} - 17))$

Step 6.4

Multiply $- 2$ by $6$ .

$- (- 6 x^{2} + 2 y^{2} + 2 y - 12 + x (y^{2} - 17))$

Step 7

Apply the distributive property.

$- (- 6 x^{2} + 2 y^{2} + 2 y - 12 + x y^{2} + x \cdot - 17)$

Step 8

Move $- 17$ to the left of $x$ .

$- (- 6 x^{2} + 2 y^{2} + 2 y - 12 + x y^{2} - 17 x)$