Basic Math Examples

$- 5 y^{2} - 5 y - 6 + (5 y^{2} - 3 y - 8) - (- 3 y^{2} - 6 y + 1)$

Step 1

Simplify by adding terms.

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Step 1.1

Remove parentheses.

$- 5 y^{2} - 5 y - 6 + 5 y^{2} - 3 y - 8 - (- 3 y^{2} - 6 y + 1)$

Step 1.2

Combine the opposite terms in $- 5 y^{2} - 5 y - 6 + 5 y^{2} - 3 y - 8 - (- 3 y^{2} - 6 y + 1)$ .

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Step 1.2.1

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

$- 5 y - 6 + 0 - 3 y - 8 - (- 3 y^{2} - 6 y + 1)$

Step 1.2.2

Add $- 5 y - 6$ and $0$ .

$- 5 y - 6 - 3 y - 8 - (- 3 y^{2} - 6 y + 1)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$- 5 y - 6 - 3 y - 8 - (- 3 y^{2}) - (- 6 y) - 1 \cdot 1$

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- 3$ by $- 1$ .

$- 5 y - 6 - 3 y - 8 + 3 y^{2} - (- 6 y) - 1 \cdot 1$

Step 2.2.2

Multiply $- 6$ by $- 1$ .

$- 5 y - 6 - 3 y - 8 + 3 y^{2} + 6 y - 1 \cdot 1$

Step 2.2.3

Multiply $- 1$ by $1$ .

$- 5 y - 6 - 3 y - 8 + 3 y^{2} + 6 y - 1$

Step 3

Simplify by adding terms.

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Step 3.1

Subtract $3 y$ from $- 5 y$ .

$- 8 y - 6 - 8 + 3 y^{2} + 6 y - 1$

Step 3.2

Add $- 8 y$ and $6 y$ .

$- 2 y - 6 - 8 + 3 y^{2} - 1$

Step 3.3

Simplify the expression.

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Step 3.3.1

Subtract $8$ from $- 6$ .

$- 2 y - 14 + 3 y^{2} - 1$

Step 3.3.2

Subtract $1$ from $- 14$ .

$- 2 y + 3 y^{2} - 15$

Step 3.3.3

Reorder $- 2 y$ and $3 y^{2}$ .

$3 y^{2} - 2 y - 15$