Basic Math Examples

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

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

Step 1

Rewrite

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

$(2 m - n) (2 m - n)$ .

$(2 m - n) (2 m - n)$

Step 2

Expand

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

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Step 2.1

Apply the distributive property.

$2 m (2 m - n) - n (2 m - n)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

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

Step 3.1.2

Multiply

$m$ by

$m$ by adding the exponents.

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Step 3.1.2.1

Move

$m$ .

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

Step 3.1.2.2

Multiply

$m$ by

$m$ .

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

Step 3.1.3

Multiply

$2$ by

$2$ .

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

Step 3.1.4

Rewrite using the commutative property of multiplication.

$4 m^{2} + 2 \cdot - 1 m n - n (2 m) - n (- n)$

Step 3.1.5

Multiply

$2$ by

$- 1$ .

$4 m^{2} - 2 m n - n (2 m) - n (- n)$

Step 3.1.6

Rewrite using the commutative property of multiplication.

$4 m^{2} - 2 m n - 1 \cdot 2 n m - n (- n)$

Step 3.1.7

Multiply

$- 1$ by

$2$ .

$4 m^{2} - 2 m n - 2 n m - n (- n)$

Step 3.1.8

Rewrite using the commutative property of multiplication.

$4 m^{2} - 2 m n - 2 n m - 1 \cdot - 1 n \cdot n$

Step 3.1.9

Multiply

$n$ by

$n$ by adding the exponents.

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Step 3.1.9.1

Move

$n$ .

$4 m^{2} - 2 m n - 2 n m - 1 \cdot - 1 (n \cdot n)$

Step 3.1.9.2

Multiply

$n$ by

$n$ .

$4 m^{2} - 2 m n - 2 n m - 1 \cdot - 1 n^{2}$

Step 3.1.10

Multiply

$- 1$ by

$- 1$ .

$4 m^{2} - 2 m n - 2 n m + 1 n^{2}$

Step 3.1.11

Multiply

$n^{2}$ by

$1$ .

$4 m^{2} - 2 m n - 2 n m + n^{2}$

Step 3.2

Subtract

$2 n m$ from

$- 2 m n$ .

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Step 3.2.1

Move

$n$ .

$4 m^{2} - 2 m n - 2 m n + n^{2}$

Step 3.2.2

Subtract

$2 m n$ from

$- 2 m n$ .

$4 m^{2} - 4 m n + n^{2}$