Basic Math Examples

$(3 m - 4 n) (3 m + 4 n - k)$

Step 1

Expand $(3 m - 4 n) (3 m + 4 n - k)$ by multiplying each term in the first expression by each term in the second expression.

$3 m (3 m) + 3 m (4 n) + 3 m (- k) - 4 n (3 m) - 4 n (4 n) - 4 n (- k)$

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.

$3 \cdot 3 m \cdot m + 3 m (4 n) + 3 m (- k) - 4 n (3 m) - 4 n (4 n) - 4 n (- k)$

Step 2.1.2

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

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Step 2.1.2.1

Move $m$ .

$3 \cdot 3 (m \cdot m) + 3 m (4 n) + 3 m (- k) - 4 n (3 m) - 4 n (4 n) - 4 n (- k)$

Step 2.1.2.2

Multiply $m$ by $m$ .

$3 \cdot 3 m^{2} + 3 m (4 n) + 3 m (- k) - 4 n (3 m) - 4 n (4 n) - 4 n (- k)$

Step 2.1.3

Multiply $3$ by $3$ .

$9 m^{2} + 3 m (4 n) + 3 m (- k) - 4 n (3 m) - 4 n (4 n) - 4 n (- k)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$9 m^{2} + 3 \cdot 4 m n + 3 m (- k) - 4 n (3 m) - 4 n (4 n) - 4 n (- k)$

Step 2.1.5

Multiply $3$ by $4$ .

$9 m^{2} + 12 m n + 3 m (- k) - 4 n (3 m) - 4 n (4 n) - 4 n (- k)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$9 m^{2} + 12 m n + 3 \cdot - 1 m k - 4 n (3 m) - 4 n (4 n) - 4 n (- k)$

Step 2.1.7

Multiply $3$ by $- 1$ .

$9 m^{2} + 12 m n - 3 m k - 4 n (3 m) - 4 n (4 n) - 4 n (- k)$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$9 m^{2} + 12 m n - 3 m k - 4 \cdot 3 n m - 4 n (4 n) - 4 n (- k)$

Step 2.1.9

Multiply $- 4$ by $3$ .

$9 m^{2} + 12 m n - 3 m k - 12 n m - 4 n (4 n) - 4 n (- k)$

Step 2.1.10

Rewrite using the commutative property of multiplication.

$9 m^{2} + 12 m n - 3 m k - 12 n m - 4 \cdot 4 n \cdot n - 4 n (- k)$

Step 2.1.11

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

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Step 2.1.11.1

Move $n$ .

$9 m^{2} + 12 m n - 3 m k - 12 n m - 4 \cdot 4 (n \cdot n) - 4 n (- k)$

Step 2.1.11.2

Multiply $n$ by $n$ .

$9 m^{2} + 12 m n - 3 m k - 12 n m - 4 \cdot 4 n^{2} - 4 n (- k)$

Step 2.1.12

Multiply $- 4$ by $4$ .

$9 m^{2} + 12 m n - 3 m k - 12 n m - 16 n^{2} - 4 n (- k)$

Step 2.1.13

Rewrite using the commutative property of multiplication.

$9 m^{2} + 12 m n - 3 m k - 12 n m - 16 n^{2} - 4 \cdot - 1 n k$

Step 2.1.14

Multiply $- 4$ by $- 1$ .

$9 m^{2} + 12 m n - 3 m k - 12 n m - 16 n^{2} + 4 n k$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Combine the opposite terms in $9 m^{2} + 12 m n - 3 m k - 12 n m - 16 n^{2} + 4 n k$ .

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Step 2.2.1.1

Reorder the factors in the terms $12 m n$ and $- 12 n m$ .

$9 m^{2} + 12 m n - 3 m k - 12 m n - 16 n^{2} + 4 n k$

Step 2.2.1.2

Subtract $12 m n$ from $12 m n$ .

$9 m^{2} - 3 m k + 0 - 16 n^{2} + 4 n k$

Step 2.2.1.3

Add $9 m^{2} - 3 m k$ and $0$ .

$9 m^{2} - 3 m k - 16 n^{2} + 4 n k$

Step 2.2.2

Reorder.

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Step 2.2.2.1

Move $m$ .

$9 m^{2} - 3 k m - 16 n^{2} + 4 n k$

Step 2.2.2.2

Move $n$ .

$9 m^{2} - 3 k m - 16 n^{2} + 4 k n$

Step 2.2.2.3

Move $- 16 n^{2}$ .

$9 m^{2} - 3 k m + 4 k n - 16 n^{2}$

Step 2.2.2.4

Move $9 m^{2}$ .

$- 3 k m + 4 k n + 9 m^{2} - 16 n^{2}$