Basic Math Examples

{(2 m - 3)}^{2}

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

Step 1

Rewrite

{(2 m - 3)}^{2}

${(2 m - 3)}^{2}$ as

(2 m - 3) (2 m - 3)

$(2 m - 3) (2 m - 3)$ .

(2 m - 3) (2 m - 3)

$(2 m - 3) (2 m - 3)$

Step 2

Expand

(2 m - 3) (2 m - 3)

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

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Step 2.1

Apply the distributive property.

2 m (2 m - 3) - 3 (2 m - 3)

$2 m (2 m - 3) - 3 (2 m - 3)$

Step 2.2

Apply the distributive property.

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

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

Step 2.3

Apply the distributive property.

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

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

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

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

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 \cdot - 3 - 3 (2 m) - 3 \cdot - 3

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

Step 3.1.2

Multiply

m

$m$ by

m

$m$ by adding the exponents.

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Step 3.1.2.1

Move

m

$m$ .

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

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

Step 3.1.2.2

Multiply

m

$m$ by

m

$m$ .

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

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

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

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

Step 3.1.3

Multiply

2

$2$ by

2

$2$ .

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

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

Step 3.1.4

Multiply

- 3

$- 3$ by

2

$2$ .

4 m^{2} - 6 m - 3 (2 m) - 3 \cdot - 3

$4 m^{2} - 6 m - 3 (2 m) - 3 \cdot - 3$

Step 3.1.5

Multiply

2

$2$ by

- 3

$- 3$ .

4 m^{2} - 6 m - 6 m - 3 \cdot - 3

$4 m^{2} - 6 m - 6 m - 3 \cdot - 3$

Step 3.1.6

Multiply

- 3

$- 3$ by

- 3

$- 3$ .

4 m^{2} - 6 m - 6 m + 9

$4 m^{2} - 6 m - 6 m + 9$

4 m^{2} - 6 m - 6 m + 9

$4 m^{2} - 6 m - 6 m + 9$

Step 3.2

Subtract

6 m

$6 m$ from

- 6 m

$- 6 m$ .

4 m^{2} - 12 m + 9

$4 m^{2} - 12 m + 9$

4 m^{2} - 12 m + 9

$4 m^{2} - 12 m + 9$