Algebra Examples

$(2 x^{2} - 4 y + 7 x y - 6 y^{2}) - (- 3 x^{2} + 5 y - 4 x y + y^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 x^{2} - 4 y + 7 x y - 6 y^{2} - (- 3 x^{2}) - (5 y) - (- 4 x y) - y^{2}$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 3$ by $- 1$ .

$2 x^{2} - 4 y + 7 x y - 6 y^{2} + 3 x^{2} - (5 y) - (- 4 x y) - y^{2}$

Step 1.2.2

Multiply $5$ by $- 1$ .

$2 x^{2} - 4 y + 7 x y - 6 y^{2} + 3 x^{2} - 5 y - (- 4 x y) - y^{2}$

Step 1.2.3

Multiply $- 4$ by $- 1$ .

$2 x^{2} - 4 y + 7 x y - 6 y^{2} + 3 x^{2} - 5 y + 4 (x y) - y^{2}$

$2 x^{2} - 4 y + 7 x y - 6 y^{2} + 3 x^{2} - 5 y + 4 x y - y^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $2 x^{2}$ and $3 x^{2}$ .

$5 x^{2} - 4 y + 7 x y - 6 y^{2} - 5 y + 4 x y - y^{2}$

Step 2.2

Subtract $5 y$ from $- 4 y$ .

$5 x^{2} + 7 x y - 6 y^{2} - 9 y + 4 x y - y^{2}$

Step 2.3

Add $7 x y$ and $4 x y$ .

$5 x^{2} + 11 x y - 6 y^{2} - 9 y - y^{2}$

Step 2.4

Subtract $y^{2}$ from $- 6 y^{2}$ .

$5 x^{2} + 11 x y - 7 y^{2} - 9 y$