Finite Math Examples

$(- 7 m^{2} + m - 9) (5 m - 8)$

Step 1

Expand $(- 7 m^{2} + m - 9) (5 m - 8)$ by multiplying each term in the first expression by each term in the second expression.

$- 7 m^{2} (5 m) - 7 m^{2} \cdot - 8 + m (5 m) + m \cdot - 8 - 9 (5 m) - 9 \cdot - 8$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$- 7 \cdot 5 m^{2} m - 7 m^{2} \cdot - 8 + m (5 m) + m \cdot - 8 - 9 (5 m) - 9 \cdot - 8$

Step 2.1.2

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

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Step 2.1.2.1

Move $m$ .

$- 7 \cdot 5 (m \cdot m^{2}) - 7 m^{2} \cdot - 8 + m (5 m) + m \cdot - 8 - 9 (5 m) - 9 \cdot - 8$

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

$- 7 \cdot 5 (m^{1} m^{2}) - 7 m^{2} \cdot - 8 + m (5 m) + m \cdot - 8 - 9 (5 m) - 9 \cdot - 8$

Step 2.1.2.2.2

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

$- 7 \cdot 5 m^{1 + 2} - 7 m^{2} \cdot - 8 + m (5 m) + m \cdot - 8 - 9 (5 m) - 9 \cdot - 8$

Step 2.1.2.3

Add $1$ and $2$ .

$- 7 \cdot 5 m^{3} - 7 m^{2} \cdot - 8 + m (5 m) + m \cdot - 8 - 9 (5 m) - 9 \cdot - 8$

Step 2.1.3

Multiply $- 7$ by $5$ .

$- 35 m^{3} - 7 m^{2} \cdot - 8 + m (5 m) + m \cdot - 8 - 9 (5 m) - 9 \cdot - 8$

Step 2.1.4

Multiply $- 8$ by $- 7$ .

$- 35 m^{3} + 56 m^{2} + m (5 m) + m \cdot - 8 - 9 (5 m) - 9 \cdot - 8$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$- 35 m^{3} + 56 m^{2} + 5 m \cdot m + m \cdot - 8 - 9 (5 m) - 9 \cdot - 8$

Step 2.1.6

Multiply $m$ by $m$ by adding the exponents.

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Step 2.1.6.1

Move $m$ .

$- 35 m^{3} + 56 m^{2} + 5 (m \cdot m) + m \cdot - 8 - 9 (5 m) - 9 \cdot - 8$

Step 2.1.6.2

Multiply $m$ by $m$ .

$- 35 m^{3} + 56 m^{2} + 5 m^{2} + m \cdot - 8 - 9 (5 m) - 9 \cdot - 8$

Step 2.1.7

Move $- 8$ to the left of $m$ .

$- 35 m^{3} + 56 m^{2} + 5 m^{2} - 8 \cdot m - 9 (5 m) - 9 \cdot - 8$

Step 2.1.8

Multiply $5$ by $- 9$ .

$- 35 m^{3} + 56 m^{2} + 5 m^{2} - 8 m - 45 m - 9 \cdot - 8$

Step 2.1.9

Multiply $- 9$ by $- 8$ .

$- 35 m^{3} + 56 m^{2} + 5 m^{2} - 8 m - 45 m + 72$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $56 m^{2}$ and $5 m^{2}$ .

$- 35 m^{3} + 61 m^{2} - 8 m - 45 m + 72$

Step 2.2.2

Subtract $45 m$ from $- 8 m$ .

$- 35 m^{3} + 61 m^{2} - 53 m + 72$