Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- - x$ .

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Step 1.2.1.1

Multiply $- 1$ by $- 1$ .

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

Step 1.2.1.2

Multiply $x$ by $1$ .

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

Step 1.2.2

Multiply $- - z$ .

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Step 1.2.2.1

Multiply $- 1$ by $- 1$ .

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

Step 1.2.2.2

Multiply $z$ by $1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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Step 2.1.1

Reorder the factors in the terms $y^{2} x$ and $- x y^{2}$ .

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

Step 2.1.2

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

$x^{2} + z + x + 0 + z$

Step 2.1.3

Add $x^{2} + z + x$ and $0$ .

$x^{2} + z + x + z$

Step 2.2

Add $z$ and $z$ .

$x^{2} + x + 2 z$