Calculus Examples

$8 w^{2} - 3 w + 9 + (9 w^{2} - 3 w + 9) - (- w^{2} + 9 w + 4)$

Step 1

Remove parentheses.

$8 w^{2} - 3 w + 9 + 9 w^{2} - 3 w + 9 - (- w^{2} + 9 w + 4)$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Simplify.

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Step 2.2.1

Multiply $- - w^{2}$ .

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Step 2.2.1.1

Multiply $- 1$ by $- 1$ .

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

Step 2.2.1.2

Multiply $w^{2}$ by $1$ .

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

Step 2.2.2

Multiply $9$ by $- 1$ .

$8 w^{2} - 3 w + 9 + 9 w^{2} - 3 w + 9 + w^{2} - 9 w - 1 \cdot 4$

Step 2.2.3

Multiply $- 1$ by $4$ .

$8 w^{2} - 3 w + 9 + 9 w^{2} - 3 w + 9 + w^{2} - 9 w - 4$

Step 3

Simplify by adding terms.

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Step 3.1

Add $8 w^{2}$ and $9 w^{2}$ .

$17 w^{2} - 3 w + 9 - 3 w + 9 + w^{2} - 9 w - 4$

Step 3.2

Add $17 w^{2}$ and $w^{2}$ .

$18 w^{2} - 3 w + 9 - 3 w + 9 - 9 w - 4$

Step 3.3

Subtract $3 w$ from $- 3 w$ .

$18 w^{2} - 6 w + 9 + 9 - 9 w - 4$

Step 3.4

Subtract $9 w$ from $- 6 w$ .

$18 w^{2} - 15 w + 9 + 9 - 4$

Step 3.5

Simplify by adding and subtracting.

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Step 3.5.1

Add $9$ and $9$ .

$18 w^{2} - 15 w + 18 - 4$

Step 3.5.2

Subtract $4$ from $18$ .

$18 w^{2} - 15 w + 14$