Basic Math Examples

$\frac{y^{2} - 4 y - 5}{y^{2} - 5 y - 6} \cdot \frac{y^{2} - 4 \cdot - 12}{y^{2} - 3 y - 10}$

Step 1

Factor $y^{2} - 4 y - 5$ using the AC method.

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Step 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 $- 5$ and whose sum is $- 4$ .

$- 5, 1$

Step 1.2

Write the factored form using these integers.

$\frac{(y - 5) (y + 1)}{y^{2} - 5 y - 6} \cdot \frac{y^{2} - 4 \cdot - 12}{y^{2} - 3 y - 10}$

Step 2

Factor $y^{2} - 5 y - 6$ using the AC method.

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Step 2.1

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 $- 6$ and whose sum is $- 5$ .

$- 6, 1$

Step 2.2

Write the factored form using these integers.

$\frac{(y - 5) (y + 1)}{(y - 6) (y + 1)} \cdot \frac{y^{2} - 4 \cdot - 12}{y^{2} - 3 y - 10}$

Step 3

Multiply $- 4$ by $- 12$ .

$\frac{(y - 5) (y + 1)}{(y - 6) (y + 1)} \cdot \frac{y^{2} + 48}{y^{2} - 3 y - 10}$

Step 4

Factor $y^{2} - 3 y - 10$ using the AC method.

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Step 4.1

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 $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Step 4.2

Write the factored form using these integers.

$\frac{(y - 5) (y + 1)}{(y - 6) (y + 1)} \cdot \frac{y^{2} + 48}{(y - 5) (y + 2)}$

Step 5

Simplify terms.

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Step 5.1

Cancel the common factor of $y - 5$ .

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Step 5.1.1

Cancel the common factor.

$\frac{(y - 5) (y + 1)}{(y - 6) (y + 1)} \cdot \frac{y^{2} + 48}{(y - 5) (y + 2)}$

Step 5.1.2

Rewrite the expression.

$\frac{y + 1}{(y - 6) (y + 1)} \cdot \frac{y^{2} + 48}{y + 2}$

Step 5.2

Multiply $\frac{y + 1}{(y - 6) (y + 1)}$ by $\frac{y^{2} + 48}{y + 2}$ .

$\frac{(y + 1) (y^{2} + 48)}{(y - 6) (y + 1) (y + 2)}$

Step 5.3

Cancel the common factor of $y + 1$ .

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Step 5.3.1

Cancel the common factor.

$\frac{(y + 1) (y^{2} + 48)}{(y - 6) (y + 1) (y + 2)}$

Step 5.3.2

Rewrite the expression.

$\frac{y^{2} + 48}{(y - 6) (y + 2)}$