Finite Math Examples

$(y - 9) (y + 2)$

Step 1

Expand $(y - 9) (y + 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$y (y + 2) - 9 (y + 2)$

Step 1.2

Apply the distributive property.

$y \cdot y + y \cdot 2 - 9 (y + 2)$

Step 1.3

Apply the distributive property.

$y \cdot y + y \cdot 2 - 9 y - 9 \cdot 2$

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 $y$ .

$y^{2} + y \cdot 2 - 9 y - 9 \cdot 2$

Step 2.1.2

Move $2$ to the left of $y$ .

$y^{2} + 2 \cdot y - 9 y - 9 \cdot 2$

Step 2.1.3

Multiply $- 9$ by $2$ .

$y^{2} + 2 y - 9 y - 18$

Step 2.2

Subtract $9 y$ from $2 y$ .

$y^{2} - 7 y - 18$

Step 3

Factor $y^{2} - 7 y - 18$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 18$ and whose sum is $- 7$ .

$- 9, 2$

Step 3.2

Write the factored form using these integers.

$(y - 9) (y + 2)$