Basic Math Examples

$6 y^{3} (6 y^{2} - 4 y + 8)$

Step 1

Apply the distributive property.

$6 y^{3} (6 y^{2}) + 6 y^{3} (- 4 y) + 6 y^{3} \cdot 8$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$6 \cdot 6 y^{3} y^{2} + 6 y^{3} (- 4 y) + 6 y^{3} \cdot 8$

Step 2.2

Rewrite using the commutative property of multiplication.

$6 \cdot 6 y^{3} y^{2} + 6 \cdot - 4 y^{3} y + 6 y^{3} \cdot 8$

Step 2.3

Multiply $8$ by $6$ .

$6 \cdot 6 y^{3} y^{2} + 6 \cdot - 4 y^{3} y + 48 y^{3}$

Step 3

Simplify each term.

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Step 3.1

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

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Step 3.1.1

Move $y^{2}$ .

$6 \cdot 6 (y^{2} y^{3}) + 6 \cdot - 4 y^{3} y + 48 y^{3}$

Step 3.1.2

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

$6 \cdot 6 y^{2 + 3} + 6 \cdot - 4 y^{3} y + 48 y^{3}$

Step 3.1.3

Add $2$ and $3$ .

$6 \cdot 6 y^{5} + 6 \cdot - 4 y^{3} y + 48 y^{3}$

Step 3.2

Multiply $6$ by $6$ .

$36 y^{5} + 6 \cdot - 4 y^{3} y + 48 y^{3}$

Step 3.3

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

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Step 3.3.1

Move $y$ .

$36 y^{5} + 6 \cdot - 4 (y \cdot y^{3}) + 48 y^{3}$

Step 3.3.2

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

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Step 3.3.2.1

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

$36 y^{5} + 6 \cdot - 4 (y^{1} y^{3}) + 48 y^{3}$

Step 3.3.2.2

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

$36 y^{5} + 6 \cdot - 4 y^{1 + 3} + 48 y^{3}$

Step 3.3.3

Add $1$ and $3$ .

$36 y^{5} + 6 \cdot - 4 y^{4} + 48 y^{3}$

Step 3.4

Multiply $6$ by $- 4$ .

$36 y^{5} - 24 y^{4} + 48 y^{3}$