Basic Math Examples

$(2 y^{2} - 18) (y + 3) (y - 3)$

Step 1

Expand $(2 y^{2} - 18) (y + 3)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(2 y^{2} (y + 3) - 18 (y + 3)) (y - 3)$

Step 1.2

Apply the distributive property.

$(2 y^{2} y + 2 y^{2} \cdot 3 - 18 (y + 3)) (y - 3)$

Step 1.3

Apply the distributive property.

$(2 y^{2} y + 2 y^{2} \cdot 3 - 18 y - 18 \cdot 3) (y - 3)$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Move $y$ .

$(2 (y \cdot y^{2}) + 2 y^{2} \cdot 3 - 18 y - 18 \cdot 3) (y - 3)$

Step 2.1.2

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

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Step 2.1.2.1

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

$(2 (y^{1} y^{2}) + 2 y^{2} \cdot 3 - 18 y - 18 \cdot 3) (y - 3)$

Step 2.1.2.2

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

$(2 y^{1 + 2} + 2 y^{2} \cdot 3 - 18 y - 18 \cdot 3) (y - 3)$

Step 2.1.3

Add $1$ and $2$ .

$(2 y^{3} + 2 y^{2} \cdot 3 - 18 y - 18 \cdot 3) (y - 3)$

Step 2.2

Multiply $3$ by $2$ .

$(2 y^{3} + 6 y^{2} - 18 y - 18 \cdot 3) (y - 3)$

Step 2.3

Multiply $- 18$ by $3$ .

$(2 y^{3} + 6 y^{2} - 18 y - 54) (y - 3)$

Step 3

Expand $(2 y^{3} + 6 y^{2} - 18 y - 54) (y - 3)$ by multiplying each term in the first expression by each term in the second expression.

$2 y^{3} y + 2 y^{3} \cdot - 3 + 6 y^{2} y + 6 y^{2} \cdot - 3 - 18 y \cdot y - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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Step 4.1.1.1

Move $y$ .

$2 (y \cdot y^{3}) + 2 y^{3} \cdot - 3 + 6 y^{2} y + 6 y^{2} \cdot - 3 - 18 y \cdot y - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.1.2

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

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Step 4.1.1.2.1

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

$2 (y^{1} y^{3}) + 2 y^{3} \cdot - 3 + 6 y^{2} y + 6 y^{2} \cdot - 3 - 18 y \cdot y - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.1.2.2

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

$2 y^{1 + 3} + 2 y^{3} \cdot - 3 + 6 y^{2} y + 6 y^{2} \cdot - 3 - 18 y \cdot y - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.1.3

Add $1$ and $3$ .

$2 y^{4} + 2 y^{3} \cdot - 3 + 6 y^{2} y + 6 y^{2} \cdot - 3 - 18 y \cdot y - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.2

Multiply $- 3$ by $2$ .

$2 y^{4} - 6 y^{3} + 6 y^{2} y + 6 y^{2} \cdot - 3 - 18 y \cdot y - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.3

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

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Step 4.1.3.1

Move $y$ .

$2 y^{4} - 6 y^{3} + 6 (y \cdot y^{2}) + 6 y^{2} \cdot - 3 - 18 y \cdot y - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.3.2

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

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Step 4.1.3.2.1

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

$2 y^{4} - 6 y^{3} + 6 (y^{1} y^{2}) + 6 y^{2} \cdot - 3 - 18 y \cdot y - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.3.2.2

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

$2 y^{4} - 6 y^{3} + 6 y^{1 + 2} + 6 y^{2} \cdot - 3 - 18 y \cdot y - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.3.3

Add $1$ and $2$ .

$2 y^{4} - 6 y^{3} + 6 y^{3} + 6 y^{2} \cdot - 3 - 18 y \cdot y - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.4

Multiply $- 3$ by $6$ .

$2 y^{4} - 6 y^{3} + 6 y^{3} - 18 y^{2} - 18 y \cdot y - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.5

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

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Step 4.1.5.1

Move $y$ .

$2 y^{4} - 6 y^{3} + 6 y^{3} - 18 y^{2} - 18 (y \cdot y) - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.5.2

Multiply $y$ by $y$ .

$2 y^{4} - 6 y^{3} + 6 y^{3} - 18 y^{2} - 18 y^{2} - 18 y \cdot - 3 - 54 y - 54 \cdot - 3$

Step 4.1.6

Multiply $- 3$ by $- 18$ .

$2 y^{4} - 6 y^{3} + 6 y^{3} - 18 y^{2} - 18 y^{2} + 54 y - 54 y - 54 \cdot - 3$

Step 4.1.7

Multiply $- 54$ by $- 3$ .

$2 y^{4} - 6 y^{3} + 6 y^{3} - 18 y^{2} - 18 y^{2} + 54 y - 54 y + 162$

Step 4.2

Simplify by adding terms.

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Step 4.2.1

Combine the opposite terms in $2 y^{4} - 6 y^{3} + 6 y^{3} - 18 y^{2} - 18 y^{2} + 54 y - 54 y + 162$ .

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Step 4.2.1.1

Add $- 6 y^{3}$ and $6 y^{3}$ .

$2 y^{4} + 0 - 18 y^{2} - 18 y^{2} + 54 y - 54 y + 162$

Step 4.2.1.2

Add $2 y^{4}$ and $0$ .

$2 y^{4} - 18 y^{2} - 18 y^{2} + 54 y - 54 y + 162$

Step 4.2.1.3

Subtract $54 y$ from $54 y$ .

$2 y^{4} - 18 y^{2} - 18 y^{2} + 0 + 162$

Step 4.2.1.4

Add $2 y^{4} - 18 y^{2} - 18 y^{2}$ and $0$ .

$2 y^{4} - 18 y^{2} - 18 y^{2} + 162$

Step 4.2.2

Subtract $18 y^{2}$ from $- 18 y^{2}$ .

$2 y^{4} - 36 y^{2} + 162$