Algebra Examples

$(6 m n - 9) (m^{2} n - 7)$

Step 1

Expand $(6 m n - 9) (m^{2} n - 7)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$6 m n (m^{2} n - 7) - 9 (m^{2} n - 7)$

Step 1.2

Apply the distributive property.

$6 m n (m^{2} n) + 6 m n \cdot - 7 - 9 (m^{2} n - 7)$

Step 1.3

Apply the distributive property.

$6 m n (m^{2} n) + 6 m n \cdot - 7 - 9 (m^{2} n) - 9 \cdot - 7$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $m^{2}$ .

$6 (m^{2} m) n \cdot n + 6 m n \cdot - 7 - 9 (m^{2} n) - 9 \cdot - 7$

Step 2.1.2

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

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Step 2.1.2.1

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

$6 (m^{2} m^{1}) n \cdot n + 6 m n \cdot - 7 - 9 (m^{2} n) - 9 \cdot - 7$

Step 2.1.2.2

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

$6 m^{2 + 1} n \cdot n + 6 m n \cdot - 7 - 9 (m^{2} n) - 9 \cdot - 7$

Step 2.1.3

Add $2$ and $1$ .

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

Step 2.2

Multiply $n$ by $n$ by adding the exponents.

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Step 2.2.1

Move $n$ .

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

Step 2.2.2

Multiply $n$ by $n$ .

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

Step 2.3

Multiply $- 7$ by $6$ .

$6 m^{3} n^{2} - 42 m n - 9 (m^{2} n) - 9 \cdot - 7$

Step 2.4

Multiply $- 9$ by $- 7$ .

$6 m^{3} n^{2} - 42 m n - 9 m^{2} n + 63$