Basic Math Examples

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

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

Step 1

Rewrite

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

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

(2 a - 3) (2 a - 3)

$(2 a - 3) (2 a - 3)$ .

(2 a - 3) (2 a - 3)

$(2 a - 3) (2 a - 3)$

Step 2

Expand

(2 a - 3) (2 a - 3)

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

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Step 2.1

Apply the distributive property.

2 a (2 a - 3) - 3 (2 a - 3)

$2 a (2 a - 3) - 3 (2 a - 3)$

Step 2.2

Apply the distributive property.

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

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

Step 2.3

Apply the distributive property.

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

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

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

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

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

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

Step 3.1.2

Multiply

a

$a$ by

a

$a$ by adding the exponents.

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Step 3.1.2.1

Move

a

$a$ .

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

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

Step 3.1.2.2

Multiply

a

$a$ by

a

$a$ .

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

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

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

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

Step 3.1.3

Multiply

2

$2$ by

2

$2$ .

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

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

Step 3.1.4

Multiply

- 3

$- 3$ by

2

$2$ .

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

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

Step 3.1.5

Multiply

2

$2$ by

- 3

$- 3$ .

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

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

Step 3.1.6

Multiply

- 3

$- 3$ by

- 3

$- 3$ .

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

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

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

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

Step 3.2

Subtract

6 a

$6 a$ from

- 6 a

$- 6 a$ .

4 a^{2} - 12 a + 9

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

4 a^{2} - 12 a + 9

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