Basic Math Examples

$6 y^{2} - y - 2 + (- 7 y^{2} + 4 y + 9) - (- 5 y^{2} + 3 y + 2)$

Step 1

Remove parentheses.

$6 y^{2} - y - 2 - 7 y^{2} + 4 y + 9 - (- 5 y^{2} + 3 y + 2)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$6 y^{2} - y - 2 - 7 y^{2} + 4 y + 9 - (- 5 y^{2}) - (3 y) - 1 \cdot 2$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- 5$ by $- 1$ .

$6 y^{2} - y - 2 - 7 y^{2} + 4 y + 9 + 5 y^{2} - (3 y) - 1 \cdot 2$

Step 2.2.2

Multiply $3$ by $- 1$ .

$6 y^{2} - y - 2 - 7 y^{2} + 4 y + 9 + 5 y^{2} - 3 y - 1 \cdot 2$

Step 2.2.3

Multiply $- 1$ by $2$ .

$6 y^{2} - y - 2 - 7 y^{2} + 4 y + 9 + 5 y^{2} - 3 y - 2$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $7 y^{2}$ from $6 y^{2}$ .

$- y^{2} - y - 2 + 4 y + 9 + 5 y^{2} - 3 y - 2$

Step 3.2

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

$4 y^{2} - y - 2 + 4 y + 9 - 3 y - 2$

Step 3.3

Add $- y$ and $4 y$ .

$4 y^{2} + 3 y - 2 + 9 - 3 y - 2$

Step 3.4

Combine the opposite terms in $4 y^{2} + 3 y - 2 + 9 - 3 y - 2$ .

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Step 3.4.1

Subtract $3 y$ from $3 y$ .

$4 y^{2} + 0 - 2 + 9 - 2$

Step 3.4.2

Add $4 y^{2}$ and $0$ .

$4 y^{2} - 2 + 9 - 2$

Step 3.5

Simplify by adding and subtracting.

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Step 3.5.1

Add $- 2$ and $9$ .

$4 y^{2} + 7 - 2$

Step 3.5.2

Subtract $2$ from $7$ .

$4 y^{2} + 5$