Basic Math Examples

$(m - n + k) (m + 6 n - 7 k)$

Step 1

Expand $(m - n + k) (m + 6 n - 7 k)$ by multiplying each term in the first expression by each term in the second expression.

$m \cdot m + m (6 n) + m (- 7 k) - n m - n (6 n) - n (- 7 k) + k m + k (6 n) + k (- 7 k)$

Step 2

Simplify each term.

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Step 2.1

Multiply $m$ by $m$ .

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

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 2.3

Rewrite using the commutative property of multiplication.

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

Step 2.4

Rewrite using the commutative property of multiplication.

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

Step 2.5

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

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Step 2.5.1

Move $n$ .

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

Step 2.5.2

Multiply $n$ by $n$ .

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

Step 2.6

Multiply $- 1$ by $6$ .

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

Step 2.7

Rewrite using the commutative property of multiplication.

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

Step 2.8

Multiply $- 1$ by $- 7$ .

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

Step 2.9

Rewrite using the commutative property of multiplication.

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

Step 2.10

Rewrite using the commutative property of multiplication.

$m^{2} + 6 m n - 7 m k - n m - 6 n^{2} + 7 n k + k m + 6 k n - 7 k \cdot k$

Step 2.11

Multiply $k$ by $k$ by adding the exponents.

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Step 2.11.1

Move $k$ .

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

Step 2.11.2

Multiply $k$ by $k$ .

$m^{2} + 6 m n - 7 m k - n m - 6 n^{2} + 7 n k + k m + 6 k n - 7 k^{2}$

Step 3

Subtract $n m$ from $6 m n$ .

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Step 3.1

Move $n$ .

$m^{2} + 6 m n - 1 m n - 7 m k - 6 n^{2} + 7 n k + k m + 6 k n - 7 k^{2}$

Step 3.2

Subtract $m n$ from $6 m n$ .

$m^{2} + 5 m n - 7 m k - 6 n^{2} + 7 n k + k m + 6 k n - 7 k^{2}$

Step 4

Add $- 7 m k$ and $k m$ .

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Step 4.1

Move $m$ .

$m^{2} + 5 m n - 6 n^{2} + 7 n k - 7 k m + k m + 6 k n - 7 k^{2}$

Step 4.2

Add $- 7 k m$ and $k m$ .

$m^{2} + 5 m n - 6 n^{2} + 7 n k - 6 k m + 6 k n - 7 k^{2}$

Step 5

Add $7 n k$ and $6 k n$ .

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Step 5.1

Move $n$ .

$m^{2} + 5 m n - 6 n^{2} + 7 k n + 6 k n - 6 k m - 7 k^{2}$

Step 5.2

Add $7 k n$ and $6 k n$ .

$m^{2} + 5 m n - 6 n^{2} + 13 k n - 6 k m - 7 k^{2}$

Step 6

Move $- 6 n^{2}$ .

$m^{2} + 5 m n + 13 k n - 6 k m - 7 k^{2} - 6 n^{2}$

Step 7

Move $5 m n$ .

$m^{2} + 13 k n - 6 k m - 7 k^{2} + 5 m n - 6 n^{2}$

Step 8

Move $m^{2}$ .

$13 k n - 6 k m - 7 k^{2} + m^{2} + 5 m n - 6 n^{2}$

Step 9

Move $13 k n$ .

$- 6 k m - 7 k^{2} + 13 k n + m^{2} + 5 m n - 6 n^{2}$

Step 10

Reorder $- 6 k m$ and $- 7 k^{2}$ .

$- 7 k^{2} - 6 k m + 13 k n + m^{2} + 5 m n - 6 n^{2}$