Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $- (- x y)$ .

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Step 2.2.1

Multiply $- 1$ by $- 1$ .

$4 x^{2} - x^{2} + 1 (x y) - 3 y^{2} + 2 x y - (- 3 x^{2} + y^{2})$

Step 2.2.2

Multiply $x$ by $1$ .

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

Step 2.3

Apply the distributive property.

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

Step 2.4

Multiply $- 3$ by $- 1$ .

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

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $x^{2}$ from $4 x^{2}$ .

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

Step 3.2

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

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

Step 3.3

Add $x y$ and $2 x y$ .

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

Step 3.4

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

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