Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Regroup terms.

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

Step 3

Apply the distributive property.

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

Step 4

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $x$ .

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

Step 4.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x \cdot - 5 - 5 + 3 (x - 5) + x$

Step 5

Multiply $- 5$ by $2$ .

$2 x^{2} - 10 x - 5 + 3 (x - 5) + x$

Step 6

Apply the distributive property.

$2 x^{2} - 10 x - 5 + 3 x + 3 \cdot - 5 + x$

Step 7

Multiply $3$ by $- 5$ .

$2 x^{2} - 10 x - 5 + 3 x - 15 + x$

Step 8

Add $3 x$ and $x$ .

$2 x^{2} - 10 x - 5 + 4 x - 15$

Step 9

Add $- 10 x$ and $4 x$ .

$2 x^{2} - 6 x - 5 - 15$

Step 10

Subtract $15$ from $- 5$ .

$2 x^{2} - 6 x - 20$

Step 11

Factor $2$ out of $2 x^{2} - 6 x - 20$ .

Tap for more steps...

Step 11.1

Factor $2$ out of $2 x^{2}$ .

$2 (x^{2}) - 6 x - 20$

Step 11.2

Factor $2$ out of $- 6 x$ .

$2 (x^{2}) + 2 (- 3 x) - 20$

Step 11.3

Factor $2$ out of $- 20$ .

$2 x^{2} + 2 (- 3 x) + 2 \cdot - 10$

Step 11.4

Factor $2$ out of $2 x^{2} + 2 (- 3 x)$ .

$2 (x^{2} - 3 x) + 2 \cdot - 10$

Step 11.5

Factor $2$ out of $2 (x^{2} - 3 x) + 2 \cdot - 10$ .

$2 (x^{2} - 3 x - 10)$

Step 12

Factor.

Tap for more steps...

Step 12.1

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

Tap for more steps...

Step 12.1.1

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

$- 5, 2$

Step 12.1.2

Write the factored form using these integers.

$2 ((x - 5) (x + 2))$

Step 12.2

Remove unnecessary parentheses.

$2 (x - 5) (x + 2)$