Algebra Examples

$\frac{4 t + 4}{t - 5} \cdot (t^{2} - t - 20)$

Step 1

Factor $4$ out of $4 t + 4$ .

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Step 1.1

Factor $4$ out of $4 t$ .

$\frac{4 (t) + 4}{t - 5} \cdot (t^{2} - t - 20)$

Step 1.2

Factor $4$ out of $4$ .

$\frac{4 (t) + 4 (1)}{t - 5} \cdot (t^{2} - t - 20)$

Step 1.3

Factor $4$ out of $4 (t) + 4 (1)$ .

$\frac{4 (t + 1)}{t - 5} \cdot (t^{2} - t - 20)$

Step 2

Multiply $\frac{4 (t + 1)}{t - 5}$ by $t^{2} - t - 20$ .

$\frac{4 (t + 1) (t^{2} - t - 20)}{t - 5}$

Step 3

Factor $t^{2} - t - 20$ 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 $- 20$ and whose sum is $- 1$ .

$- 5, 4$

Step 3.2

Write the factored form using these integers.

$\frac{4 (t + 1) ((t - 5) (t + 4))}{t - 5}$

$\frac{4 (t + 1) (t - 5) (t + 4)}{t - 5}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $t - 5$ .

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Step 4.1.1

Cancel the common factor.

$\frac{4 (t + 1) (t - 5) (t + 4)}{t - 5}$

Step 4.1.2

Divide $4 (t + 1) (t + 4)$ by $1$ .

$4 (t + 1) (t + 4)$

Step 4.2

Apply the distributive property.

$(4 t + 4 \cdot 1) (t + 4)$

Step 4.3

Multiply $4$ by $1$ .

$(4 t + 4) (t + 4)$

Step 5

Expand $(4 t + 4) (t + 4)$ using the FOIL Method.

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Step 5.1

Apply the distributive property.

$4 t (t + 4) + 4 (t + 4)$

Step 5.2

Apply the distributive property.

$4 t \cdot t + 4 t \cdot 4 + 4 (t + 4)$

Step 5.3

Apply the distributive property.

$4 t \cdot t + 4 t \cdot 4 + 4 t + 4 \cdot 4$

Step 6

Simplify and combine like terms.

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Step 6.1

Simplify each term.

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Step 6.1.1

Multiply $t$ by $t$ by adding the exponents.

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Step 6.1.1.1

Move $t$ .

$4 (t \cdot t) + 4 t \cdot 4 + 4 t + 4 \cdot 4$

Step 6.1.1.2

Multiply $t$ by $t$ .

$4 t^{2} + 4 t \cdot 4 + 4 t + 4 \cdot 4$

Step 6.1.2

Multiply $4$ by $4$ .

$4 t^{2} + 16 t + 4 t + 4 \cdot 4$

Step 6.1.3

Multiply $4$ by $4$ .

$4 t^{2} + 16 t + 4 t + 16$

Step 6.2

Add $16 t$ and $4 t$ .

$4 t^{2} + 20 t + 16$