Basic Math Examples

$6 y (14 y - 5) \cdot (3 y (5 + 3 y))$

Step 1

Multiply $y$ by $y$ by adding the exponents.

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Step 1.1

Move $y$ .

$6 (y \cdot y) (14 y - 5) \cdot (3 (5 + 3 y))$

Step 1.2

Multiply $y$ by $y$ .

$6 y^{2} (14 y - 5) \cdot (3 (5 + 3 y))$

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

$(6 y^{2} (14 y) + 6 y^{2} \cdot - 5) \cdot (3 (5 + 3 y))$

Step 2.2

Simplify the expression.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$(6 \cdot 14 y^{2} y + 6 y^{2} \cdot - 5) \cdot (3 (5 + 3 y))$

Step 2.2.2

Multiply $- 5$ by $6$ .

$(6 \cdot 14 y^{2} y - 30 y^{2}) \cdot (3 (5 + 3 y))$

Step 2.3

Simplify each term.

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Step 2.3.1

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

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Step 2.3.1.1

Move $y$ .

$(6 \cdot 14 (y \cdot y^{2}) - 30 y^{2}) \cdot (3 (5 + 3 y))$

Step 2.3.1.2

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

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Step 2.3.1.2.1

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

$(6 \cdot 14 (y^{1} y^{2}) - 30 y^{2}) \cdot (3 (5 + 3 y))$

Step 2.3.1.2.2

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

$(6 \cdot 14 y^{1 + 2} - 30 y^{2}) \cdot (3 (5 + 3 y))$

Step 2.3.1.3

Add $1$ and $2$ .

$(6 \cdot 14 y^{3} - 30 y^{2}) \cdot (3 (5 + 3 y))$

Step 2.3.2

Multiply $6$ by $14$ .

$(84 y^{3} - 30 y^{2}) \cdot (3 (5 + 3 y))$

Step 2.4

Simplify by multiplying through.

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Step 2.4.1

Apply the distributive property.

$(84 y^{3} - 30 y^{2}) \cdot (3 \cdot 5 + 3 (3 y))$

Step 2.4.2

Multiply.

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Step 2.4.2.1

Multiply $3$ by $5$ .

$(84 y^{3} - 30 y^{2}) \cdot (15 + 3 (3 y))$

Step 2.4.2.2

Multiply $3$ by $3$ .

$(84 y^{3} - 30 y^{2}) \cdot (15 + 9 y)$

Step 3

Expand $(84 y^{3} - 30 y^{2}) (15 + 9 y)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$84 y^{3} (15 + 9 y) - 30 y^{2} (15 + 9 y)$

Step 3.2

Apply the distributive property.

$84 y^{3} \cdot 15 + 84 y^{3} (9 y) - 30 y^{2} (15 + 9 y)$

Step 3.3

Apply the distributive property.

$84 y^{3} \cdot 15 + 84 y^{3} (9 y) - 30 y^{2} \cdot 15 - 30 y^{2} (9 y)$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $15$ by $84$ .

$1260 y^{3} + 84 y^{3} (9 y) - 30 y^{2} \cdot 15 - 30 y^{2} (9 y)$

Step 4.1.2

Rewrite using the commutative property of multiplication.

$1260 y^{3} + 84 \cdot 9 y^{3} y - 30 y^{2} \cdot 15 - 30 y^{2} (9 y)$

Step 4.1.3

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

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Step 4.1.3.1

Move $y$ .

$1260 y^{3} + 84 \cdot 9 (y \cdot y^{3}) - 30 y^{2} \cdot 15 - 30 y^{2} (9 y)$

Step 4.1.3.2

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

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Step 4.1.3.2.1

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

$1260 y^{3} + 84 \cdot 9 (y^{1} y^{3}) - 30 y^{2} \cdot 15 - 30 y^{2} (9 y)$

Step 4.1.3.2.2

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

$1260 y^{3} + 84 \cdot 9 y^{1 + 3} - 30 y^{2} \cdot 15 - 30 y^{2} (9 y)$

Step 4.1.3.3

Add $1$ and $3$ .

$1260 y^{3} + 84 \cdot 9 y^{4} - 30 y^{2} \cdot 15 - 30 y^{2} (9 y)$

Step 4.1.4

Multiply $84$ by $9$ .

$1260 y^{3} + 756 y^{4} - 30 y^{2} \cdot 15 - 30 y^{2} (9 y)$

Step 4.1.5

Multiply $15$ by $- 30$ .

$1260 y^{3} + 756 y^{4} - 450 y^{2} - 30 y^{2} (9 y)$

Step 4.1.6

Rewrite using the commutative property of multiplication.

$1260 y^{3} + 756 y^{4} - 450 y^{2} - 30 \cdot 9 y^{2} y$

Step 4.1.7

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

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Step 4.1.7.1

Move $y$ .

$1260 y^{3} + 756 y^{4} - 450 y^{2} - 30 \cdot 9 (y \cdot y^{2})$

Step 4.1.7.2

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

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Step 4.1.7.2.1

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

$1260 y^{3} + 756 y^{4} - 450 y^{2} - 30 \cdot 9 (y^{1} y^{2})$

Step 4.1.7.2.2

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

$1260 y^{3} + 756 y^{4} - 450 y^{2} - 30 \cdot 9 y^{1 + 2}$

Step 4.1.7.3

Add $1$ and $2$ .

$1260 y^{3} + 756 y^{4} - 450 y^{2} - 30 \cdot 9 y^{3}$

Step 4.1.8

Multiply $- 30$ by $9$ .

$1260 y^{3} + 756 y^{4} - 450 y^{2} - 270 y^{3}$

Step 4.2

Subtract $270 y^{3}$ from $1260 y^{3}$ .

$990 y^{3} + 756 y^{4} - 450 y^{2}$

Step 5

Reorder $990 y^{3}$ and $756 y^{4}$ .

$756 y^{4} + 990 y^{3} - 450 y^{2}$