Finite Math Examples

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

Step 1

Simplify terms.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Simplify the expression.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

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

Step 1.2.2

Multiply $5$ by $1$ .

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

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $y^{4}$ by $y$ by adding the exponents.

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Step 1.3.1.1

Move $y$ .

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

Step 1.3.1.2

Multiply $y$ by $y^{4}$ .

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Step 1.3.1.2.1

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

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

Step 1.3.1.2.2

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

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

Step 1.3.1.3

Add $1$ and $4$ .

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

Step 1.3.2

Multiply $5$ by $3$ .

$(15 y^{5} + 5 y^{4}) (y - 1)$

Step 2

Expand $(15 y^{5} + 5 y^{4}) (y - 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$15 y^{5} (y - 1) + 5 y^{4} (y - 1)$

Step 2.2

Apply the distributive property.

$15 y^{5} y + 15 y^{5} \cdot - 1 + 5 y^{4} (y - 1)$

Step 2.3

Apply the distributive property.

$15 y^{5} y + 15 y^{5} \cdot - 1 + 5 y^{4} y + 5 y^{4} \cdot - 1$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $y^{5}$ by $y$ by adding the exponents.

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Step 3.1.1.1

Move $y$ .

$15 (y \cdot y^{5}) + 15 y^{5} \cdot - 1 + 5 y^{4} y + 5 y^{4} \cdot - 1$

Step 3.1.1.2

Multiply $y$ by $y^{5}$ .

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Step 3.1.1.2.1

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

$15 (y^{1} y^{5}) + 15 y^{5} \cdot - 1 + 5 y^{4} y + 5 y^{4} \cdot - 1$

Step 3.1.1.2.2

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

$15 y^{1 + 5} + 15 y^{5} \cdot - 1 + 5 y^{4} y + 5 y^{4} \cdot - 1$

Step 3.1.1.3

Add $1$ and $5$ .

$15 y^{6} + 15 y^{5} \cdot - 1 + 5 y^{4} y + 5 y^{4} \cdot - 1$

Step 3.1.2

Multiply $- 1$ by $15$ .

$15 y^{6} - 15 y^{5} + 5 y^{4} y + 5 y^{4} \cdot - 1$

Step 3.1.3

Multiply $y^{4}$ by $y$ by adding the exponents.

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Step 3.1.3.1

Move $y$ .

$15 y^{6} - 15 y^{5} + 5 (y \cdot y^{4}) + 5 y^{4} \cdot - 1$

Step 3.1.3.2

Multiply $y$ by $y^{4}$ .

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Step 3.1.3.2.1

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

$15 y^{6} - 15 y^{5} + 5 (y^{1} y^{4}) + 5 y^{4} \cdot - 1$

Step 3.1.3.2.2

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

$15 y^{6} - 15 y^{5} + 5 y^{1 + 4} + 5 y^{4} \cdot - 1$

Step 3.1.3.3

Add $1$ and $4$ .

$15 y^{6} - 15 y^{5} + 5 y^{5} + 5 y^{4} \cdot - 1$

Step 3.1.4

Multiply $- 1$ by $5$ .

$15 y^{6} - 15 y^{5} + 5 y^{5} - 5 y^{4}$

Step 3.2

Add $- 15 y^{5}$ and $5 y^{5}$ .

$15 y^{6} - 10 y^{5} - 5 y^{4}$