Algebra Examples

$21 x y - 12 b^{2} + 14 x b - 18$ by

Step 1

Regroup terms.

$- 18 + 21 x y - 12 b^{2} + 14 x b$

Step 2

Add parentheses.

$- 18 + 21 (x y) - 12 b^{2} + 14 (x b)$

Step 3

Let $u = x y$ . Substitute $u$ for all occurrences of $x y$ .

$- 18 + 21 u - 12 b^{2} + 14 x b$

Step 4

Factor $- 1$ out of $21 u - 12 b^{2} + 14 x b$ .

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Step 4.1

Reorder the expression.

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Step 4.1.1

Move $x$ .

$- 18 + 21 u - 12 b^{2} + 14 b x$

Step 4.1.2

Move $21 u$ .

$- 18 - 12 b^{2} + 14 b x + 21 u$

Step 4.1.3

Reorder $- 12 b^{2}$ and $14 b x$ .

$- 18 + 14 b x - 12 b^{2} + 21 u$

Step 4.2

Factor $- 1$ out of $14 b x$ .

$- 18 - (- 14 b x) - 12 b^{2} + 21 u$

Step 4.3

Factor $- 1$ out of $- 12 b^{2}$ .

$- 18 - (- 14 b x) - (12 b^{2}) + 21 u$

Step 4.4

Factor $- 1$ out of $21 u$ .

$- 18 - (- 14 b x) - (12 b^{2}) - (- 21 u)$

Step 4.5

Factor $- 1$ out of $- (- 14 b x) - (12 b^{2})$ .

$- 18 - (- 14 b x + 12 b^{2}) - (- 21 u)$

Step 4.6

Factor $- 1$ out of $- (- 14 b x + 12 b^{2}) - (- 21 u)$ .

$- 18 - (- 14 b x + 12 b^{2} - 21 u)$

Step 5

Replace all occurrences of $u$ with $x y$ .

$- 18 - (- 14 b x + 12 b^{2} - 21 (x y))$

Step 6

Remove parentheses.

$- 18 - (- 14 b x + 12 b^{2} - 21 x y)$

Step 7

Factor $- 1$ out of $- 18 - (- 14 b x + 12 b^{2} - 21 x y)$ .

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Step 7.1

Reorder the expression.

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Step 7.1.1

Move $12 b^{2}$ .

$- 18 - (- 14 b x - 21 x y + 12 b^{2})$

Step 7.1.2

Reorder $- 14 b x$ and $- 21 x y$ .

$- 18 - (- 21 x y - 14 b x + 12 b^{2})$

Step 7.1.3

Reorder $- 18$ and $- (- 21 x y - 14 b x + 12 b^{2})$ .

$- (- 21 x y - 14 b x + 12 b^{2}) - 18$

Step 7.2

Rewrite $- 18$ as $- 1 (18)$ .

$- (- 21 x y - 14 b x + 12 b^{2}) - 1 (18)$

Step 7.3

Factor $- 1$ out of $- (- 21 x y - 14 b x + 12 b^{2}) - 1 (18)$ .

$- (- 21 x y - 14 b x + 12 b^{2} + 18)$