Algebra Examples

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

Step 1

Simplify by adding terms.

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Step 1.1

Remove parentheses.

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

Step 1.2

Combine the opposite terms in $(2 x^{2} + 3 y^{2} - z^{2}) - (x^{2} - y^{2} - z^{2}) + 4 x^{2} - 3 y^{2}$ .

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Step 1.2.1

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

$(2 x^{2} - z^{2}) - (x^{2} - y^{2} - z^{2}) + 4 x^{2} + 0$

Step 1.2.2

Add $(2 x^{2} - z^{2}) - (x^{2} - y^{2} - z^{2}) + 4 x^{2}$ and $0$ .

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- - y^{2}$ .

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Step 2.2.1.1

Multiply $- 1$ by $- 1$ .

$2 x^{2} - z^{2} - x^{2} + 1 y^{2} - - z^{2} + 4 x^{2}$

Step 2.2.1.2

Multiply $y^{2}$ by $1$ .

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

Step 2.2.2

Multiply $- - z^{2}$ .

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Step 2.2.2.1

Multiply $- 1$ by $- 1$ .

$2 x^{2} - z^{2} - x^{2} + y^{2} + 1 z^{2} + 4 x^{2}$

Step 2.2.2.2

Multiply $z^{2}$ by $1$ .

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

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $2 x^{2} - z^{2} - x^{2} + y^{2} + z^{2} + 4 x^{2}$ .

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Step 3.1.1

Add $- z^{2}$ and $z^{2}$ .

$2 x^{2} - x^{2} + y^{2} + 0 + 4 x^{2}$

Step 3.1.2

Add $2 x^{2} - x^{2} + y^{2}$ and $0$ .

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

Step 3.2

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

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

Step 3.3

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

$5 x^{2} + y^{2}$