Basic Math Examples

$(m - n - 5) (m - n + 5)$

Step 1

Expand $(m - n - 5) (m - n + 5)$ by multiplying each term in the first expression by each term in the second expression.

$m \cdot m + m (- n) + m \cdot 5 - n m - n (- n) - n \cdot 5 - 5 m - 5 (- n) - 5 \cdot 5$

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Combine the opposite terms in $m \cdot m + m (- n) + m \cdot 5 - n m - n (- n) - n \cdot 5 - 5 m - 5 (- n) - 5 \cdot 5$ .

Tap for more steps...

Step 2.1.1

Reorder the factors in the terms $m \cdot 5$ and $- 5 m$ .

$m \cdot m + m (- n) + 5 m - n m - n (- n) - n \cdot 5 - 5 m - 5 (- n) - 5 \cdot 5$

Step 2.1.2

Subtract $5 m$ from $5 m$ .

$m \cdot m + m (- n) - n m - n (- n) - n \cdot 5 + 0 - 5 (- n) - 5 \cdot 5$

Step 2.1.3

Add $m \cdot m + m (- n) - n m - n (- n) - n \cdot 5$ and $0$ .

$m \cdot m + m (- n) - n m - n (- n) - n \cdot 5 - 5 (- n) - 5 \cdot 5$

Step 2.2

Simplify each term.

Tap for more steps...

Step 2.2.1

Multiply $m$ by $m$ .

$m^{2} + m (- n) - n m - n (- n) - n \cdot 5 - 5 (- n) - 5 \cdot 5$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$m^{2} - m n - n m - n (- n) - n \cdot 5 - 5 (- n) - 5 \cdot 5$

Step 2.2.3

Rewrite using the commutative property of multiplication.

$m^{2} - m n - n m - 1 \cdot - 1 n \cdot n - n \cdot 5 - 5 (- n) - 5 \cdot 5$

Step 2.2.4

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

Tap for more steps...

Step 2.2.4.1

Move $n$ .

$m^{2} - m n - n m - 1 \cdot - 1 (n \cdot n) - n \cdot 5 - 5 (- n) - 5 \cdot 5$

Step 2.2.4.2

Multiply $n$ by $n$ .

$m^{2} - m n - n m - 1 \cdot - 1 n^{2} - n \cdot 5 - 5 (- n) - 5 \cdot 5$

Step 2.2.5

Multiply $- 1$ by $- 1$ .

$m^{2} - m n - n m + 1 n^{2} - n \cdot 5 - 5 (- n) - 5 \cdot 5$

Step 2.2.6

Multiply $n^{2}$ by $1$ .

$m^{2} - m n - n m + n^{2} - n \cdot 5 - 5 (- n) - 5 \cdot 5$

Step 2.2.7

Multiply $5$ by $- 1$ .

$m^{2} - m n - n m + n^{2} - 5 n - 5 (- n) - 5 \cdot 5$

Step 2.2.8

Multiply $- 1$ by $- 5$ .

$m^{2} - m n - n m + n^{2} - 5 n + 5 n - 5 \cdot 5$

Step 2.2.9

Multiply $- 5$ by $5$ .

$m^{2} - m n - n m + n^{2} - 5 n + 5 n - 25$

Step 2.3

Combine the opposite terms in $m^{2} - m n - n m + n^{2} - 5 n + 5 n - 25$ .

Tap for more steps...

Step 2.3.1

Add $- 5 n$ and $5 n$ .

$m^{2} - m n - n m + n^{2} + 0 - 25$

Step 2.3.2

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

$m^{2} - m n - n m + n^{2} - 25$

Step 3

Subtract $n m$ from $- m n$ .

Tap for more steps...

Step 3.1

Move $n$ .

$m^{2} - m n - 1 m n + n^{2} - 25$

Step 3.2

Subtract $m n$ from $- m n$ .

$m^{2} - 2 m n + n^{2} - 25$