Basic Math Examples

$3 y^{2} \sqrt{4 z^{4}} (y + 2 z) + 2 z^{2}$

Step 1

Rewrite $4 z^{4}$ as ${(2 z^{2})}^{2}$ .

$3 y^{2} \sqrt{{(2 z^{2})}^{2}} (y + 2 z) + 2 z^{2}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Multiply $3$ by $2$ .

$6 y^{2} z^{2} (y + 2 z) + 2 z^{2}$

Step 5

Apply the distributive property.

$6 y^{2} z^{2} y + 6 y^{2} z^{2} (2 z) + 2 z^{2}$

Step 6

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

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Step 6.1

Move $y$ .

$6 (y \cdot y^{2}) z^{2} + 6 y^{2} z^{2} (2 z) + 2 z^{2}$

Step 6.2

Multiply $y$ by $y^{2}$ .

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Step 6.2.1

Raise $y$ to the power of $1$ .

$6 (y^{1} y^{2}) z^{2} + 6 y^{2} z^{2} (2 z) + 2 z^{2}$

Step 6.2.2

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

$6 y^{1 + 2} z^{2} + 6 y^{2} z^{2} (2 z) + 2 z^{2}$

Step 6.3

Add $1$ and $2$ .

$6 y^{3} z^{2} + 6 y^{2} z^{2} (2 z) + 2 z^{2}$

Step 7

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

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Step 7.1

Move $z$ .

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

Step 7.2

Multiply $z$ by $z^{2}$ .

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Step 7.2.1

Raise $z$ to the power of $1$ .

$6 y^{3} z^{2} + 6 y^{2} (z^{1} z^{2}) \cdot 2 + 2 z^{2}$

Step 7.2.2

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

$6 y^{3} z^{2} + 6 y^{2} z^{1 + 2} \cdot 2 + 2 z^{2}$

Step 7.3

Add $1$ and $2$ .

$6 y^{3} z^{2} + 6 y^{2} z^{3} \cdot 2 + 2 z^{2}$

Step 8

Multiply $2$ by $6$ .

$6 y^{3} z^{2} + 12 y^{2} z^{3} + 2 z^{2}$