Algebra Examples

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

Step 1

Factor $a - b$ out of $(a - b) (x^{2} - 5) - (a - b) (3 x + 5)$ .

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Step 1.1

Factor $a - b$ out of $- (a - b) (3 x + 5)$ .

$(a - b) (x^{2} - 5) + (a - b) (- 1 (3 x + 5))$

Step 1.2

Factor $a - b$ out of $(a - b) (x^{2} - 5) + (a - b) (- 1 (3 x + 5))$ .

$(a - b) (x^{2} - 5 - 1 (3 x + 5))$

Step 2

Apply the distributive property.

$(a - b) (x^{2} - 5 - 1 (3 x) - 1 \cdot 5)$

Step 3

Multiply $3$ by $- 1$ .

$(a - b) (x^{2} - 5 - 3 x - 1 \cdot 5)$

Step 4

Multiply $- 1$ by $5$ .

$(a - b) (x^{2} - 5 - 3 x - 5)$

Step 5

Subtract $5$ from $- 5$ .

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

Step 6

Factor.

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Step 6.1

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

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Step 6.1.1

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 6.1.2

Write the factored form using these integers.

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

Step 6.2

Remove unnecessary parentheses.

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