Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply $2$ by $- 1$ .

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

Step 1.2.2

Multiply $3$ by $- 1$ .

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

Step 1.2.3

Multiply $- 2$ by $- 1$ .

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

Step 1.2.4

Multiply $2$ by $- 1$ .

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

Step 1.3

Remove parentheses.

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

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $3 x^{2} y^{2}$ from $- 3 x^{2} y^{2}$ .

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

Step 2.2

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

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

Step 2.3

Add $- 4 x y^{2}$ and $2 x y^{2}$ .

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