Basic Math Examples

$2 y^{2} - 5 z y + y^{2} - (y^{2} - 3 z^{2} + 2 y z)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 y^{2} - 5 z y + y^{2} - y^{2} - (- 3 z^{2}) - (2 y z)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 3$ by $- 1$ .

$2 y^{2} - 5 z y + y^{2} - y^{2} + 3 z^{2} - (2 y z)$

Step 1.2.2

Multiply $2$ by $- 1$ .

$2 y^{2} - 5 z y + y^{2} - y^{2} + 3 z^{2} - 2 (y z)$

$2 y^{2} - 5 z y + y^{2} - y^{2} + 3 z^{2} - 2 y z$

Step 2

Combine the opposite terms in $2 y^{2} - 5 z y + y^{2} - y^{2} + 3 z^{2} - 2 y z$ .

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Step 2.1

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

$2 y^{2} - 5 z y + 0 + 3 z^{2} - 2 y z$

Step 2.2

Add $2 y^{2} - 5 z y$ and $0$ .

$2 y^{2} - 5 z y + 3 z^{2} - 2 y z$

Step 3

Subtract $2 y z$ from $- 5 z y$ .

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Step 3.1

Move $z$ .

$2 y^{2} + 3 z^{2} - 5 y z - 2 y z$

Step 3.2

Subtract $2 y z$ from $- 5 y z$ .

$2 y^{2} + 3 z^{2} - 7 y z$