Basic Math Examples

$3 y^{2} (4 y^{5} + 8 y)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$3 y^{2} (4 y^{5}) + 3 y^{2} (8 y)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 4 y^{2} y^{5} + 3 y^{2} (8 y)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$3 \cdot 4 y^{2} y^{5} + 3 \cdot 8 y^{2} y$

Step 2

Simplify each term.

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Step 2.1

Multiply $y^{2}$ by $y^{5}$ by adding the exponents.

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Step 2.1.1

Move $y^{5}$ .

$3 \cdot 4 (y^{5} y^{2}) + 3 \cdot 8 y^{2} y$

Step 2.1.2

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

$3 \cdot 4 y^{5 + 2} + 3 \cdot 8 y^{2} y$

Step 2.1.3

Add $5$ and $2$ .

$3 \cdot 4 y^{7} + 3 \cdot 8 y^{2} y$

Step 2.2

Multiply $3$ by $4$ .

$12 y^{7} + 3 \cdot 8 y^{2} y$

Step 2.3

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

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Step 2.3.1

Move $y$ .

$12 y^{7} + 3 \cdot 8 (y \cdot y^{2})$

Step 2.3.2

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

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Step 2.3.2.1

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

$12 y^{7} + 3 \cdot 8 (y^{1} y^{2})$

Step 2.3.2.2

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

$12 y^{7} + 3 \cdot 8 y^{1 + 2}$

Step 2.3.3

Add $1$ and $2$ .

$12 y^{7} + 3 \cdot 8 y^{3}$

Step 2.4

Multiply $3$ by $8$ .

$12 y^{7} + 24 y^{3}$