Basic Math Examples

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

Step 1

Expand $(y + 5) (y - 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $y \cdot y + y \cdot - 5 + 5 y + 5 \cdot - 5$ .

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Step 2.1.1

Reorder the factors in the terms $y \cdot - 5$ and $5 y$ .

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

Step 2.1.2

Add $- 5 y$ and $5 y$ .

$(y \cdot y + 0 + 5 \cdot - 5) (y + 1)$

Step 2.1.3

Add $y \cdot y$ and $0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $y$ by $y$ .

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

Step 2.2.2

Multiply $5$ by $- 5$ .

$(y^{2} - 25) (y + 1)$

Step 3

Expand $(y^{2} - 25) (y + 1)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$y^{2} (y + 1) - 25 (y + 1)$

Step 3.2

Apply the distributive property.

$y^{2} y + y^{2} \cdot 1 - 25 (y + 1)$

Step 3.3

Apply the distributive property.

$y^{2} y + y^{2} \cdot 1 - 25 y - 25 \cdot 1$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

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

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Step 4.1.1.1

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

$y^{2} y^{1} + y^{2} \cdot 1 - 25 y - 25 \cdot 1$

Step 4.1.1.2

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

$y^{2 + 1} + y^{2} \cdot 1 - 25 y - 25 \cdot 1$

Step 4.1.2

Add $2$ and $1$ .

$y^{3} + y^{2} \cdot 1 - 25 y - 25 \cdot 1$

Step 4.2

Multiply $y^{2}$ by $1$ .

$y^{3} + y^{2} - 25 y - 25 \cdot 1$

Step 4.3

Multiply $- 25$ by $1$ .

$y^{3} + y^{2} - 25 y - 25$