Basic Math Examples

$- 7 (7 q^{2} - 7 q + 3) + 6 (- q^{2} + 9 q - 9)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 7 (7 q^{2}) - 7 (- 7 q) - 7 \cdot 3 + 6 (- q^{2} + 9 q - 9)$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $7$ by $- 7$ .

$- 49 q^{2} - 7 (- 7 q) - 7 \cdot 3 + 6 (- q^{2} + 9 q - 9)$

Step 1.2.2

Multiply $- 7$ by $- 7$ .

$- 49 q^{2} + 49 q - 7 \cdot 3 + 6 (- q^{2} + 9 q - 9)$

Step 1.2.3

Multiply $- 7$ by $3$ .

$- 49 q^{2} + 49 q - 21 + 6 (- q^{2} + 9 q - 9)$

Step 1.3

Apply the distributive property.

$- 49 q^{2} + 49 q - 21 + 6 (- q^{2}) + 6 (9 q) + 6 \cdot - 9$

Step 1.4

Simplify.

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Step 1.4.1

Multiply $- 1$ by $6$ .

$- 49 q^{2} + 49 q - 21 - 6 q^{2} + 6 (9 q) + 6 \cdot - 9$

Step 1.4.2

Multiply $9$ by $6$ .

$- 49 q^{2} + 49 q - 21 - 6 q^{2} + 54 q + 6 \cdot - 9$

Step 1.4.3

Multiply $6$ by $- 9$ .

$- 49 q^{2} + 49 q - 21 - 6 q^{2} + 54 q - 54$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $6 q^{2}$ from $- 49 q^{2}$ .

$- 55 q^{2} + 49 q - 21 + 54 q - 54$

Step 2.2

Add $49 q$ and $54 q$ .

$- 55 q^{2} + 103 q - 21 - 54$

Step 2.3

Subtract $54$ from $- 21$ .

$- 55 q^{2} + 103 q - 75$