Basic Math Examples

$\frac{t^{2} + 2 t - 35}{t^{2} + 3 t - 40} \cdot \frac{t^{2} - 4 t - 32}{t^{2} + 11 t + 28}$

Step 1

Factor $t^{2} + 2 t - 35$ 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 $- 35$ and whose sum is $2$ .

$- 5, 7$

Step 1.2

Write the factored form using these integers.

$\frac{(t - 5) (t + 7)}{t^{2} + 3 t - 40} \cdot \frac{t^{2} - 4 t - 32}{t^{2} + 11 t + 28}$

Step 2

Factor $t^{2} + 3 t - 40$ 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 $- 40$ and whose sum is $3$ .

$- 5, 8$

Step 2.2

Write the factored form using these integers.

$\frac{(t - 5) (t + 7)}{(t - 5) (t + 8)} \cdot \frac{t^{2} - 4 t - 32}{t^{2} + 11 t + 28}$

Step 3

Factor $t^{2} - 4 t - 32$ 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 $- 32$ and whose sum is $- 4$ .

$- 8, 4$

Step 3.2

Write the factored form using these integers.

$\frac{(t - 5) (t + 7)}{(t - 5) (t + 8)} \cdot \frac{(t - 8) (t + 4)}{t^{2} + 11 t + 28}$

Step 4

Factor $t^{2} + 11 t + 28$ 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 $28$ and whose sum is $11$ .

$4, 7$

Step 4.2

Write the factored form using these integers.

$\frac{(t - 5) (t + 7)}{(t - 5) (t + 8)} \cdot \frac{(t - 8) (t + 4)}{(t + 4) (t + 7)}$

Step 5

Simplify terms.

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Step 5.1

Cancel the common factor of $t + 7$ .

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Step 5.1.1

Factor $t + 7$ out of $(t - 5) (t + 7)$ .

$\frac{(t + 7) (t - 5)}{(t - 5) (t + 8)} \cdot \frac{(t - 8) (t + 4)}{(t + 4) (t + 7)}$

Step 5.1.2

Factor $t + 7$ out of $(t + 4) (t + 7)$ .

$\frac{(t + 7) (t - 5)}{(t - 5) (t + 8)} \cdot \frac{(t - 8) (t + 4)}{(t + 7) (t + 4)}$

Step 5.1.3

Cancel the common factor.

$\frac{(t + 7) (t - 5)}{(t - 5) (t + 8)} \cdot \frac{(t - 8) (t + 4)}{(t + 7) (t + 4)}$

Step 5.1.4

Rewrite the expression.

$\frac{t - 5}{(t - 5) (t + 8)} \cdot \frac{(t - 8) (t + 4)}{t + 4}$

Step 5.2

Multiply $\frac{t - 5}{(t - 5) (t + 8)}$ by $\frac{(t - 8) (t + 4)}{t + 4}$ .

$\frac{(t - 5) ((t - 8) (t + 4))}{(t - 5) (t + 8) (t + 4)}$

Step 5.3

Cancel the common factor of $t - 5$ .

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Step 5.3.1

Cancel the common factor.

$\frac{(t - 5) ((t - 8) (t + 4))}{(t - 5) (t + 8) (t + 4)}$

Step 5.3.2

Rewrite the expression.

$\frac{(t - 8) (t + 4)}{(t + 8) (t + 4)}$

Step 5.4

Cancel the common factor of $t + 4$ .

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Step 5.4.1

Cancel the common factor.

$\frac{(t - 8) (t + 4)}{(t + 8) (t + 4)}$

Step 5.4.2

Rewrite the expression.

$\frac{t - 8}{t + 8}$