Basic Math Examples

${(6 + 3 v)}^{2}$

Step 1

Rewrite ${(6 + 3 v)}^{2}$ as $(6 + 3 v) (6 + 3 v)$ .

$(6 + 3 v) (6 + 3 v)$

Step 2

Expand $(6 + 3 v) (6 + 3 v)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$6 (6 + 3 v) + 3 v (6 + 3 v)$

Step 2.2

Apply the distributive property.

$6 \cdot 6 + 6 (3 v) + 3 v (6 + 3 v)$

Step 2.3

Apply the distributive property.

$6 \cdot 6 + 6 (3 v) + 3 v \cdot 6 + 3 v (3 v)$

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

Multiply $6$ by $6$ .

$36 + 6 (3 v) + 3 v \cdot 6 + 3 v (3 v)$

Step 3.1.2

Multiply $3$ by $6$ .

$36 + 18 v + 3 v \cdot 6 + 3 v (3 v)$

Step 3.1.3

Multiply $6$ by $3$ .

$36 + 18 v + 18 v + 3 v (3 v)$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$36 + 18 v + 18 v + 3 \cdot 3 v \cdot v$

Step 3.1.5

Multiply $v$ by $v$ by adding the exponents.

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Step 3.1.5.1

Move $v$ .

$36 + 18 v + 18 v + 3 \cdot 3 (v \cdot v)$

Step 3.1.5.2

Multiply $v$ by $v$ .

$36 + 18 v + 18 v + 3 \cdot 3 v^{2}$

Step 3.1.6

Multiply $3$ by $3$ .

$36 + 18 v + 18 v + 9 v^{2}$

Step 3.2

Add $18 v$ and $18 v$ .

$36 + 36 v + 9 v^{2}$