Basic Math Examples

$- 3 y^{2} - 8 y + 4 + (2 y^{2} \cdot (9 y) + 3) - (2 y^{2} - 8 y - 8)$

Step 1

Remove parentheses.

$- 3 y^{2} - 8 y + 4 + 2 y^{2} \cdot (9 y) + 3 - (2 y^{2} - 8 y - 8)$

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$- 3 y^{2} - 8 y + 4 + 2 \cdot 9 y^{2} y + 3 - (2 y^{2} - 8 y - 8)$

Step 2.2

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 2.2.1

Move $y$ .

$- 3 y^{2} - 8 y + 4 + 2 \cdot 9 (y \cdot y^{2}) + 3 - (2 y^{2} - 8 y - 8)$

Step 2.2.2

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

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Step 2.2.2.1

Raise $y$ to the power of $1$ .

$- 3 y^{2} - 8 y + 4 + 2 \cdot 9 (y^{1} y^{2}) + 3 - (2 y^{2} - 8 y - 8)$

Step 2.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 3 y^{2} - 8 y + 4 + 2 \cdot 9 y^{1 + 2} + 3 - (2 y^{2} - 8 y - 8)$

Step 2.2.3

Add $1$ and $2$ .

$- 3 y^{2} - 8 y + 4 + 2 \cdot 9 y^{3} + 3 - (2 y^{2} - 8 y - 8)$

Step 2.3

Multiply $2$ by $9$ .

$- 3 y^{2} - 8 y + 4 + 18 y^{3} + 3 - (2 y^{2} - 8 y - 8)$

Step 2.4

Apply the distributive property.

$- 3 y^{2} - 8 y + 4 + 18 y^{3} + 3 - (2 y^{2}) - (- 8 y) - - 8$

Step 2.5

Simplify.

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Step 2.5.1

Multiply $2$ by $- 1$ .

$- 3 y^{2} - 8 y + 4 + 18 y^{3} + 3 - 2 y^{2} - (- 8 y) - - 8$

Step 2.5.2

Multiply $- 8$ by $- 1$ .

$- 3 y^{2} - 8 y + 4 + 18 y^{3} + 3 - 2 y^{2} + 8 y - - 8$

Step 2.5.3

Multiply $- 1$ by $- 8$ .

$- 3 y^{2} - 8 y + 4 + 18 y^{3} + 3 - 2 y^{2} + 8 y + 8$

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $- 3 y^{2} - 8 y + 4 + 18 y^{3} + 3 - 2 y^{2} + 8 y + 8$ .

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Step 3.1.1

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

$- 3 y^{2} + 4 + 18 y^{3} + 3 - 2 y^{2} + 0 + 8$

Step 3.1.2

Add $- 3 y^{2} + 4 + 18 y^{3} + 3 - 2 y^{2}$ and $0$ .

$- 3 y^{2} + 4 + 18 y^{3} + 3 - 2 y^{2} + 8$

Step 3.2

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

$- 5 y^{2} + 4 + 18 y^{3} + 3 + 8$

Step 3.3

Simplify the expression.

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Step 3.3.1

Add $4$ and $3$ .

$- 5 y^{2} + 18 y^{3} + 7 + 8$

Step 3.3.2

Add $7$ and $8$ .

$- 5 y^{2} + 18 y^{3} + 15$

Step 3.3.3

Reorder $- 5 y^{2}$ and $18 y^{3}$ .

$18 y^{3} - 5 y^{2} + 15$