Basic Math Examples

$y^{2} z^{3} + y z^{2} - 30 z$

Step 1

Factor $z$ out of $y^{2} z^{3} + y z^{2} - 30 z$ .

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Step 1.1

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

$z (y^{2} z^{2}) + y z^{2} - 30 z$

Step 1.2

Factor $z$ out of $y z^{2}$ .

$z (y^{2} z^{2}) + z (y z) - 30 z$

Step 1.3

Factor $z$ out of $- 30 z$ .

$z (y^{2} z^{2}) + z (y z) + z \cdot - 30$

Step 1.4

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

$z (y^{2} z^{2} + y z) + z \cdot - 30$

Step 1.5

Factor $z$ out of $z (y^{2} z^{2} + y z) + z \cdot - 30$ .

$z (y^{2} z^{2} + y z - 30)$

Step 2

Rewrite $y^{2} z^{2}$ as ${(y z)}^{2}$ .

$z ({(y z)}^{2} + y z - 30)$

Step 3

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

$z (u^{2} + u - 30)$

Step 4

Factor $u^{2} + u - 30$ using the AC method.

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Step 4.1

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 $- 30$ and whose sum is $1$ .

$- 5, 6$

Step 4.2

Write the factored form using these integers.

$z ((u - 5) (u + 6))$

Step 5

Factor.

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Step 5.1

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

$z ((y z - 5) (y z + 6))$

Step 5.2

Remove unnecessary parentheses.

$z (y z - 5) (y z + 6)$