Pre-Algebra Examples

$\frac{1}{2} y^{2} - \frac{3}{2} y - 20$

Step 1

Factor $\frac{1}{2}$ out of each term.

$\frac{1}{2} (y^{2} - 1 \cdot 3 y - 40)$

Step 2

Multiply $- 1$ by $3 y$ .

$\frac{1}{2} \cdot (y^{2} - 1 (3 y) - 40)$

Step 3

Multiply $3$ by $- 1$ .

$\frac{1}{2} \cdot (y^{2} - 3 y - 40)$

Step 4

Factor.

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Step 4.1

Factor $y^{2} - 3 y - 40$ using the AC method.

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Step 4.1.1

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 $- 40$ and whose sum is $- 3$ .

$- 8, 5$

Step 4.1.2

Write the factored form using these integers.

$\frac{1}{2} \cdot ((y - 8) (y + 5))$

Step 4.2

Remove unnecessary parentheses.

$\frac{1}{2} \cdot (y - 8) (y + 5)$