Basic Math Examples

$(y + 3) (y + 1) (y - 2) (y - 5)$

Step 1

Expand $(y + 3) (y + 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(y (y + 1) + 3 (y + 1)) (y - 2) (y - 5)$

Step 1.2

Apply the distributive property.

$(y \cdot y + y \cdot 1 + 3 (y + 1)) (y - 2) (y - 5)$

Step 1.3

Apply the distributive property.

$(y \cdot y + y \cdot 1 + 3 y + 3 \cdot 1) (y - 2) (y - 5)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $y$ by $y$ .

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

Step 2.1.2

Multiply $y$ by $1$ .

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

Step 2.1.3

Multiply $3$ by $1$ .

$(y^{2} + y + 3 y + 3) (y - 2) (y - 5)$

Step 2.2

Add $y$ and $3 y$ .

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

Step 3

Expand $(y^{2} + 4 y + 3) (y - 2)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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Step 4.1.1.1

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

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Step 4.1.1.1.1

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

$(y^{2} y^{1} + y^{2} \cdot - 2 + 4 y \cdot y + 4 y \cdot - 2 + 3 y + 3 \cdot - 2) (y - 5)$

Step 4.1.1.1.2

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

$(y^{2 + 1} + y^{2} \cdot - 2 + 4 y \cdot y + 4 y \cdot - 2 + 3 y + 3 \cdot - 2) (y - 5)$

Step 4.1.1.2

Add $2$ and $1$ .

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

Step 4.1.2

Move $- 2$ to the left of $y^{2}$ .

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

Step 4.1.3

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

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Step 4.1.3.1

Move $y$ .

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

Step 4.1.3.2

Multiply $y$ by $y$ .

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

Step 4.1.4

Multiply $- 2$ by $4$ .

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

Step 4.1.5

Multiply $3$ by $- 2$ .

$(y^{3} - 2 y^{2} + 4 y^{2} - 8 y + 3 y - 6) (y - 5)$

Step 4.2

Simplify by adding terms.

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Step 4.2.1

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

$(y^{3} + 2 y^{2} - 8 y + 3 y - 6) (y - 5)$

Step 4.2.2

Add $- 8 y$ and $3 y$ .

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

Step 5

Expand $(y^{3} + 2 y^{2} - 5 y - 6) (y - 5)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 6

Simplify terms.

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Step 6.1

Simplify each term.

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Step 6.1.1

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

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Step 6.1.1.1

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

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Step 6.1.1.1.1

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

$y^{3} y^{1} + y^{3} \cdot - 5 + 2 y^{2} y + 2 y^{2} \cdot - 5 - 5 y \cdot y - 5 y \cdot - 5 - 6 y - 6 \cdot - 5$

Step 6.1.1.1.2

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

$y^{3 + 1} + y^{3} \cdot - 5 + 2 y^{2} y + 2 y^{2} \cdot - 5 - 5 y \cdot y - 5 y \cdot - 5 - 6 y - 6 \cdot - 5$

Step 6.1.1.2

Add $3$ and $1$ .

$y^{4} + y^{3} \cdot - 5 + 2 y^{2} y + 2 y^{2} \cdot - 5 - 5 y \cdot y - 5 y \cdot - 5 - 6 y - 6 \cdot - 5$

Step 6.1.2

Move $- 5$ to the left of $y^{3}$ .

$y^{4} - 5 \cdot y^{3} + 2 y^{2} y + 2 y^{2} \cdot - 5 - 5 y \cdot y - 5 y \cdot - 5 - 6 y - 6 \cdot - 5$

Step 6.1.3

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

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Step 6.1.3.1

Move $y$ .

$y^{4} - 5 y^{3} + 2 (y \cdot y^{2}) + 2 y^{2} \cdot - 5 - 5 y \cdot y - 5 y \cdot - 5 - 6 y - 6 \cdot - 5$

Step 6.1.3.2

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

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Step 6.1.3.2.1

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

$y^{4} - 5 y^{3} + 2 (y^{1} y^{2}) + 2 y^{2} \cdot - 5 - 5 y \cdot y - 5 y \cdot - 5 - 6 y - 6 \cdot - 5$

Step 6.1.3.2.2

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

$y^{4} - 5 y^{3} + 2 y^{1 + 2} + 2 y^{2} \cdot - 5 - 5 y \cdot y - 5 y \cdot - 5 - 6 y - 6 \cdot - 5$

Step 6.1.3.3

Add $1$ and $2$ .

$y^{4} - 5 y^{3} + 2 y^{3} + 2 y^{2} \cdot - 5 - 5 y \cdot y - 5 y \cdot - 5 - 6 y - 6 \cdot - 5$

Step 6.1.4

Multiply $- 5$ by $2$ .

$y^{4} - 5 y^{3} + 2 y^{3} - 10 y^{2} - 5 y \cdot y - 5 y \cdot - 5 - 6 y - 6 \cdot - 5$

Step 6.1.5

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

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Step 6.1.5.1

Move $y$ .

$y^{4} - 5 y^{3} + 2 y^{3} - 10 y^{2} - 5 (y \cdot y) - 5 y \cdot - 5 - 6 y - 6 \cdot - 5$

Step 6.1.5.2

Multiply $y$ by $y$ .

$y^{4} - 5 y^{3} + 2 y^{3} - 10 y^{2} - 5 y^{2} - 5 y \cdot - 5 - 6 y - 6 \cdot - 5$

Step 6.1.6

Multiply $- 5$ by $- 5$ .

$y^{4} - 5 y^{3} + 2 y^{3} - 10 y^{2} - 5 y^{2} + 25 y - 6 y - 6 \cdot - 5$

Step 6.1.7

Multiply $- 6$ by $- 5$ .

$y^{4} - 5 y^{3} + 2 y^{3} - 10 y^{2} - 5 y^{2} + 25 y - 6 y + 30$

Step 6.2

Simplify by adding terms.

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Step 6.2.1

Add $- 5 y^{3}$ and $2 y^{3}$ .

$y^{4} - 3 y^{3} - 10 y^{2} - 5 y^{2} + 25 y - 6 y + 30$

Step 6.2.2

Subtract $5 y^{2}$ from $- 10 y^{2}$ .

$y^{4} - 3 y^{3} - 15 y^{2} + 25 y - 6 y + 30$

Step 6.2.3

Subtract $6 y$ from $25 y$ .

$y^{4} - 3 y^{3} - 15 y^{2} + 19 y + 30$