Basic Math Examples

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

Step 1

Remove parentheses.

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

Step 2

Simplify each term.

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Step 2.1

Raise $4$ to the power of $2$ .

$- 6 w^{2} - 4 w - 7 - 1 \cdot 16 - 9 w + 9 - (5 w^{2} - 7 w - 7)$

Step 2.2

Multiply $- 1$ by $16$ .

$- 6 w^{2} - 4 w - 7 - 16 - 9 w + 9 - (5 w^{2} - 7 w - 7)$

Step 2.3

Apply the distributive property.

$- 6 w^{2} - 4 w - 7 - 16 - 9 w + 9 - (5 w^{2}) - (- 7 w) - - 7$

Step 2.4

Simplify.

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Step 2.4.1

Multiply $5$ by $- 1$ .

$- 6 w^{2} - 4 w - 7 - 16 - 9 w + 9 - 5 w^{2} - (- 7 w) - - 7$

Step 2.4.2

Multiply $- 7$ by $- 1$ .

$- 6 w^{2} - 4 w - 7 - 16 - 9 w + 9 - 5 w^{2} + 7 w - - 7$

Step 2.4.3

Multiply $- 1$ by $- 7$ .

$- 6 w^{2} - 4 w - 7 - 16 - 9 w + 9 - 5 w^{2} + 7 w + 7$

Step 3

Simplify by adding terms.

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Step 3.1

Combine the opposite terms in $- 6 w^{2} - 4 w - 7 - 16 - 9 w + 9 - 5 w^{2} + 7 w + 7$ .

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Step 3.1.1

Add $- 7$ and $7$ .

$- 6 w^{2} - 4 w - 16 - 9 w + 9 - 5 w^{2} + 7 w + 0$

Step 3.1.2

Add $- 6 w^{2} - 4 w - 16 - 9 w + 9 - 5 w^{2} + 7 w$ and $0$ .

$- 6 w^{2} - 4 w - 16 - 9 w + 9 - 5 w^{2} + 7 w$

Step 3.2

Subtract $5 w^{2}$ from $- 6 w^{2}$ .

$- 11 w^{2} - 4 w - 16 - 9 w + 9 + 7 w$

Step 3.3

Subtract $9 w$ from $- 4 w$ .

$- 11 w^{2} - 13 w - 16 + 9 + 7 w$

Step 3.4

Add $- 13 w$ and $7 w$ .

$- 11 w^{2} - 6 w - 16 + 9$

Step 3.5

Add $- 16$ and $9$ .

$- 11 w^{2} - 6 w - 7$