Basic Math Examples

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

Step 1

Expand $(2 v^{2} + 3 z^{2}) (2 v^{2} + 3 z^{2})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 2 v^{2} v^{2} + 2 v^{2} (3 z^{2}) + 3 z^{2} (2 v^{2}) + 3 z^{2} (3 z^{2})$

Step 2.1.2

Multiply $v^{2}$ by $v^{2}$ by adding the exponents.

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Step 2.1.2.1

Move $v^{2}$ .

$2 \cdot 2 (v^{2} v^{2}) + 2 v^{2} (3 z^{2}) + 3 z^{2} (2 v^{2}) + 3 z^{2} (3 z^{2})$

Step 2.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot 2 v^{2 + 2} + 2 v^{2} (3 z^{2}) + 3 z^{2} (2 v^{2}) + 3 z^{2} (3 z^{2})$

Step 2.1.2.3

Add $2$ and $2$ .

$2 \cdot 2 v^{4} + 2 v^{2} (3 z^{2}) + 3 z^{2} (2 v^{2}) + 3 z^{2} (3 z^{2})$

Step 2.1.3

Multiply $2$ by $2$ .

$4 v^{4} + 2 v^{2} (3 z^{2}) + 3 z^{2} (2 v^{2}) + 3 z^{2} (3 z^{2})$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$4 v^{4} + 2 \cdot 3 v^{2} z^{2} + 3 z^{2} (2 v^{2}) + 3 z^{2} (3 z^{2})$

Step 2.1.5

Multiply $2$ by $3$ .

$4 v^{4} + 6 v^{2} z^{2} + 3 z^{2} (2 v^{2}) + 3 z^{2} (3 z^{2})$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$4 v^{4} + 6 v^{2} z^{2} + 3 \cdot 2 z^{2} v^{2} + 3 z^{2} (3 z^{2})$

Step 2.1.7

Multiply $3$ by $2$ .

$4 v^{4} + 6 v^{2} z^{2} + 6 z^{2} v^{2} + 3 z^{2} (3 z^{2})$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$4 v^{4} + 6 v^{2} z^{2} + 6 z^{2} v^{2} + 3 \cdot 3 z^{2} z^{2}$

Step 2.1.9

Multiply $z^{2}$ by $z^{2}$ by adding the exponents.

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Step 2.1.9.1

Move $z^{2}$ .

$4 v^{4} + 6 v^{2} z^{2} + 6 z^{2} v^{2} + 3 \cdot 3 (z^{2} z^{2})$

Step 2.1.9.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 v^{4} + 6 v^{2} z^{2} + 6 z^{2} v^{2} + 3 \cdot 3 z^{2 + 2}$

Step 2.1.9.3

Add $2$ and $2$ .

$4 v^{4} + 6 v^{2} z^{2} + 6 z^{2} v^{2} + 3 \cdot 3 z^{4}$

Step 2.1.10

Multiply $3$ by $3$ .

$4 v^{4} + 6 v^{2} z^{2} + 6 z^{2} v^{2} + 9 z^{4}$

Step 2.2

Add $6 v^{2} z^{2}$ and $6 z^{2} v^{2}$ .

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Step 2.2.1

Move $z^{2}$ .

$4 v^{4} + 6 v^{2} z^{2} + 6 v^{2} z^{2} + 9 z^{4}$

Step 2.2.2

Add $6 v^{2} z^{2}$ and $6 v^{2} z^{2}$ .

$4 v^{4} + 12 v^{2} z^{2} + 9 z^{4}$