Basic Math Examples

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

Step 1

Rewrite

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

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

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

Step 2

Expand

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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.

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

Step 3.1.2

Multiply

$a$ by

$a$ by adding the exponents.

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Step 3.1.2.1

Move

$a$ .

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

Step 3.1.2.2

Multiply

$a$ by

$a$ .

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

Step 3.1.3

Multiply

$3$ by

$3$ .

$9 a^{2} + 3 a \cdot - 2 - 2 (3 a) - 2 \cdot - 2$

Step 3.1.4

Multiply

$- 2$ by

$3$ .

$9 a^{2} - 6 a - 2 (3 a) - 2 \cdot - 2$

Step 3.1.5

Multiply

$3$ by

$- 2$ .

$9 a^{2} - 6 a - 6 a - 2 \cdot - 2$

Step 3.1.6

Multiply

$- 2$ by

$- 2$ .

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

Step 3.2

Subtract

$6 a$ from

$- 6 a$ .

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