Basic Math Examples

$2 {(3 y - z)}^{2} - 2 (3 y - z) - 4$

Step 1

Factor $2$ out of $2 {(3 y - z)}^{2} - 2 (3 y - z) - 4$ .

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Step 1.1

Factor $2$ out of $2 {(3 y - z)}^{2}$ .

$2 ({(3 y - z)}^{2}) - 2 (3 y - z) - 4$

Step 1.2

Factor $2$ out of $- 2 (3 y - z)$ .

$2 ({(3 y - z)}^{2}) + 2 (- (3 y - z)) - 4$

Step 1.3

Factor $2$ out of $- 4$ .

$2 ({(3 y - z)}^{2}) + 2 (- (3 y - z)) + 2 (- 2)$

Step 1.4

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

$2 ({(3 y - z)}^{2} - (3 y - z)) + 2 (- 2)$

Step 1.5

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

$2 ({(3 y - z)}^{2} - (3 y - z) - 2)$

Step 2

Let $u = 3 y - z$ . Substitute $u$ for all occurrences of $3 y - z$ .

$2 (u^{2} - u - 2)$

Step 3

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

$- 2, 1$

Step 3.2

Write the factored form using these integers.

$2 ((u - 2) (u + 1))$

Step 4

Factor.

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Step 4.1

Replace all occurrences of $u$ with $3 y - z$ .

$2 ((3 y - z - 2) (3 y - z + 1))$

Step 4.2

Remove unnecessary parentheses.

$2 (3 y - z - 2) (3 y - z + 1)$