Finite Math Examples

$2 y^{2} (3 x + 5 y)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$2 y^{2} (3 x) + 2 y^{2} (5 y)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$2 \cdot 3 y^{2} x + 2 y^{2} (5 y)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$2 \cdot 3 y^{2} x + 2 \cdot 5 y^{2} y$

Step 2

Simplify each term.

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Step 2.1

Multiply $2$ by $3$ .

$6 y^{2} x + 2 \cdot 5 y^{2} y$

Step 2.2

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

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Step 2.2.1

Move $y$ .

$6 y^{2} x + 2 \cdot 5 (y \cdot y^{2})$

Step 2.2.2

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

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Step 2.2.2.1

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

$6 y^{2} x + 2 \cdot 5 (y^{1} y^{2})$

Step 2.2.2.2

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

$6 y^{2} x + 2 \cdot 5 y^{1 + 2}$

Step 2.2.3

Add $1$ and $2$ .

$6 y^{2} x + 2 \cdot 5 y^{3}$

Step 2.3

Multiply $2$ by $5$ .

$6 y^{2} x + 10 y^{3}$