Basic Math Examples

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

Step 1

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

$(v + 2 z) (v + 2 z)$

Step 2

Expand $(v + 2 z) (v + 2 z)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$v (v + 2 z) + 2 z (v + 2 z)$

Step 2.2

Apply the distributive property.

$v \cdot v + v (2 z) + 2 z (v + 2 z)$

Step 2.3

Apply the distributive property.

$v \cdot v + v (2 z) + 2 z v + 2 z (2 z)$

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 $v$ by $v$ .

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

Step 3.1.2

Rewrite using the commutative property of multiplication.

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

Step 3.1.3

Rewrite using the commutative property of multiplication.

$v^{2} + 2 v z + 2 z v + 2 \cdot 2 z \cdot z$

Step 3.1.4

Multiply $z$ by $z$ by adding the exponents.

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Step 3.1.4.1

Move $z$ .

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

Step 3.1.4.2

Multiply $z$ by $z$ .

$v^{2} + 2 v z + 2 z v + 2 \cdot 2 z^{2}$

Step 3.1.5

Multiply $2$ by $2$ .

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

Step 3.2

Add $2 v z$ and $2 z v$ .

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Step 3.2.1

Move $z$ .

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

Step 3.2.2

Add $2 v z$ and $2 v z$ .

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