Basic Math Examples

$6 y^{3} (8 y^{3} + 9 y)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$6 y^{3} (8 y^{3}) + 6 y^{3} (9 y)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$6 \cdot 8 y^{3} y^{3} + 6 y^{3} (9 y)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$6 \cdot 8 y^{3} y^{3} + 6 \cdot 9 y^{3} y$

Step 2

Simplify each term.

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Step 2.1

Multiply $y^{3}$ by $y^{3}$ by adding the exponents.

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Step 2.1.1

Move $y^{3}$ .

$6 \cdot 8 (y^{3} y^{3}) + 6 \cdot 9 y^{3} y$

Step 2.1.2

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

$6 \cdot 8 y^{3 + 3} + 6 \cdot 9 y^{3} y$

Step 2.1.3

Add $3$ and $3$ .

$6 \cdot 8 y^{6} + 6 \cdot 9 y^{3} y$

Step 2.2

Multiply $6$ by $8$ .

$48 y^{6} + 6 \cdot 9 y^{3} y$

Step 2.3

Multiply $y^{3}$ by $y$ by adding the exponents.

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Step 2.3.1

Move $y$ .

$48 y^{6} + 6 \cdot 9 (y \cdot y^{3})$

Step 2.3.2

Multiply $y$ by $y^{3}$ .

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Step 2.3.2.1

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

$48 y^{6} + 6 \cdot 9 (y^{1} y^{3})$

Step 2.3.2.2

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

$48 y^{6} + 6 \cdot 9 y^{1 + 3}$

Step 2.3.3

Add $1$ and $3$ .

$48 y^{6} + 6 \cdot 9 y^{4}$

Step 2.4

Multiply $6$ by $9$ .

$48 y^{6} + 54 y^{4}$