Algebra Examples

$(m - 3 n) (m + 2 n) - m (m - n)$

Step 1

Simplify each term.

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Step 1.1

Expand $(m - 3 n) (m + 2 n)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$m (m + 2 n) - 3 n (m + 2 n) - m (m - n)$

Step 1.1.2

Apply the distributive property.

$m \cdot m + m (2 n) - 3 n (m + 2 n) - m (m - n)$

Step 1.1.3

Apply the distributive property.

$m \cdot m + m (2 n) - 3 n m - 3 n (2 n) - m (m - n)$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $m$ by $m$ .

$m^{2} + m (2 n) - 3 n m - 3 n (2 n) - m (m - n)$

Step 1.2.1.2

Rewrite using the commutative property of multiplication.

$m^{2} + 2 m n - 3 n m - 3 n (2 n) - m (m - n)$

Step 1.2.1.3

Rewrite using the commutative property of multiplication.

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

Step 1.2.1.4

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

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Step 1.2.1.4.1

Move $n$ .

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

Step 1.2.1.4.2

Multiply $n$ by $n$ .

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

Step 1.2.1.5

Multiply $- 3$ by $2$ .

$m^{2} + 2 m n - 3 n m - 6 n^{2} - m (m - n)$

Step 1.2.2

Subtract $3 n m$ from $2 m n$ .

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Step 1.2.2.1

Move $n$ .

$m^{2} + 2 m n - 3 m n - 6 n^{2} - m (m - n)$

Step 1.2.2.2

Subtract $3 m n$ from $2 m n$ .

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

Step 1.3

Apply the distributive property.

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

Step 1.4

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

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Step 1.4.1

Move $m$ .

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

Step 1.4.2

Multiply $m$ by $m$ .

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

Step 1.5

Rewrite using the commutative property of multiplication.

$m^{2} - m n - 6 n^{2} - m^{2} - 1 \cdot - 1 m n$

Step 1.6

Simplify each term.

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

$m^{2} - m n - 6 n^{2} - m^{2} + 1 m n$

Step 1.6.2

Multiply $m$ by $1$ .

$m^{2} - m n - 6 n^{2} - m^{2} + m n$

Step 2

Combine the opposite terms in $m^{2} - m n - 6 n^{2} - m^{2} + m n$ .

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Step 2.1

Subtract $m^{2}$ from $m^{2}$ .

$- m n - 6 n^{2} + 0 + m n$

Step 2.2

Add $- m n - 6 n^{2}$ and $0$ .

$- m n - 6 n^{2} + m n$

Step 2.3

Add $- m n$ and $m n$ .

$- 6 n^{2} + 0$

Step 2.4

Add $- 6 n^{2}$ and $0$ .

$- 6 n^{2}$