Finite Math Examples

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

Step 1

Remove parentheses.

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

Step 2

Apply the distributive property.

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

Step 3

Rewrite using the commutative property of multiplication.

$5 \cdot 2 y \cdot y + 5 y \cdot - 3 + 2 y - 3$

Step 4

Multiply $- 3$ by $5$ .

$5 \cdot 2 y \cdot y - 15 y + 2 y - 3$

Step 5

Simplify each term.

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Step 5.1

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

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Step 5.1.1

Move $y$ .

$5 \cdot 2 (y \cdot y) - 15 y + 2 y - 3$

Step 5.1.2

Multiply $y$ by $y$ .

$5 \cdot 2 y^{2} - 15 y + 2 y - 3$

Step 5.2

Multiply $5$ by $2$ .

$10 y^{2} - 15 y + 2 y - 3$

Step 6

Add $- 15 y$ and $2 y$ .

$10 y^{2} - 13 y - 3$

Step 7

Factor by grouping.

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Step 7.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 10 \cdot - 3 = - 30$ and whose sum is $b = - 13$ .

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Step 7.1.1

Factor $- 13$ out of $- 13 y$ .

$10 y^{2} - 13 (y) - 3$

Step 7.1.2

Rewrite $- 13$ as $2$ plus $- 15$

$10 y^{2} + (2 - 15) y - 3$

Step 7.1.3

Apply the distributive property.

$10 y^{2} + 2 y - 15 y - 3$

Step 7.2

Factor out the greatest common factor from each group.

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Step 7.2.1

Group the first two terms and the last two terms.

$(10 y^{2} + 2 y) - 15 y - 3$

Step 7.2.2

Factor out the greatest common factor (GCF) from each group.

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

Step 7.3

Factor the polynomial by factoring out the greatest common factor, $5 y + 1$ .

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