Algebra Examples

$(15 x^{2} + 11 x y - 19 y^{2}) - (6 x^{2} - 3 x y)$

Step 1

Regroup terms.

$- 19 y^{2} + 15 x^{2} + 11 x y - (6 x^{2} - 3 x y)$

Step 2

Apply the distributive property.

$- 19 y^{2} + 15 x^{2} + 11 x y - (6 x^{2}) - (- 3 x y)$

Step 3

Multiply $6$ by $- 1$ .

$- 19 y^{2} + 15 x^{2} + 11 x y - 6 x^{2} - (- 3 x y)$

Step 4

Multiply $- 3$ by $- 1$ .

$- 19 y^{2} + 15 x^{2} + 11 x y - 6 x^{2} + 3 (x y)$

Step 5

Remove parentheses.

$- 19 y^{2} + 15 x^{2} + 11 x y - 6 x^{2} + 3 x y$

Step 6

Subtract $6 x^{2}$ from $15 x^{2}$ .

$- 19 y^{2} + 9 x^{2} + 11 x y + 3 x y$

Step 7

Add $11 x y$ and $3 x y$ .

$- 19 y^{2} + 9 x^{2} + 14 x y$

Step 8

Factor $x$ out of $9 x^{2} + 14 x y$ .

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Step 8.1

Factor $x$ out of $9 x^{2}$ .

$- 19 y^{2} + x (9 x) + 14 x y$

Step 8.2

Factor $x$ out of $14 x y$ .

$- 19 y^{2} + x (9 x) + x (14 y)$

Step 8.3

Factor $x$ out of $x (9 x) + x (14 y)$ .

$- 19 y^{2} + x (9 x + 14 y)$

Step 9

Factor $- 1$ out of $- 19 y^{2} + x (9 x + 14 y)$ .

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Step 9.1

Reorder $- 19 y^{2}$ and $x (9 x + 14 y)$ .

$x (9 x + 14 y) - 19 y^{2}$

Step 9.2

Factor $- 1$ out of $x (9 x + 14 y)$ .

$- (- x (9 x + 14 y)) - 19 y^{2}$

Step 9.3

Factor $- 1$ out of $- 19 y^{2}$ .

$- (- x (9 x + 14 y)) - (19 y^{2})$

Step 9.4

Factor $- 1$ out of $- (- x (9 x + 14 y)) - (19 y^{2})$ .

$- (- x (9 x + 14 y) + 19 y^{2})$

Step 10

Apply the distributive property.

$- (- x (9 x) - x (14 y) + 19 y^{2})$

Step 11

Rewrite using the commutative property of multiplication.

$- (- 1 \cdot 9 x \cdot x - x (14 y) + 19 y^{2})$

Step 12

Rewrite using the commutative property of multiplication.

$- (- 1 \cdot 9 x \cdot x - 1 \cdot 14 x y + 19 y^{2})$

Step 13

Simplify each term.

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Step 13.1

Multiply $x$ by $x$ by adding the exponents.

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Step 13.1.1

Move $x$ .

$- (- 1 \cdot 9 (x \cdot x) - 1 \cdot 14 x y + 19 y^{2})$

Step 13.1.2

Multiply $x$ by $x$ .

$- (- 1 \cdot 9 x^{2} - 1 \cdot 14 x y + 19 y^{2})$

Step 13.2

Multiply $- 1$ by $9$ .

$- (- 9 x^{2} - 1 \cdot 14 x y + 19 y^{2})$

Step 13.3

Multiply $- 1$ by $14$ .

$- (- 9 x^{2} - 14 x y + 19 y^{2})$

Step 14

Factor.

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Step 14.1

Factor $- 1$ out of $- 9 x^{2} - 14 x y + 19 y^{2}$ .

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Step 14.1.1

Factor $- 1$ out of $- 9 x^{2}$ .

$- (- (9 x^{2}) - 14 x y + 19 y^{2})$

Step 14.1.2

Factor $- 1$ out of $- 14 x y$ .

$- (- (9 x^{2}) - (14 x y) + 19 y^{2})$

Step 14.1.3

Factor $- 1$ out of $19 y^{2}$ .

$- (- (9 x^{2}) - (14 x y) - (- 19 y^{2}))$

Step 14.1.4

Factor $- 1$ out of $- (9 x^{2}) - (14 x y)$ .

$- (- (9 x^{2} + 14 x y) - (- 19 y^{2}))$

Step 14.1.5

Factor $- 1$ out of $- (9 x^{2} + 14 x y) - (- 19 y^{2})$ .

$- - (9 x^{2} + 14 x y - 19 y^{2})$

Step 14.2

Remove unnecessary parentheses.

$- - 1 (9 x^{2} + 14 x y - 19 y^{2})$

Step 15

Combine exponents.

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Step 15.1

Factor out negative.

$- - (9 x^{2} + 14 x y - 19 y^{2})$

Step 15.2

Multiply $- 1$ by $- 1$ .

$1 (9 x^{2} + 14 x y - 19 y^{2})$

Step 15.3

Multiply $9 x^{2} + 14 x y - 19 y^{2}$ by $1$ .

$9 x^{2} + 14 x y - 19 y^{2}$