Basic Math Examples

2 y^{4} z^{2} - 6 y^{3} z + (2 y^{4} z^{2} - y^{3} z) - (6 y^{4} z^{2} - y^{3} z)

$2 y^{4} z^{2} - 6 y^{3} z + (2 y^{4} z^{2} - y^{3} z) - (6 y^{4} z^{2} - y^{3} z)$

Step 1

Remove parentheses.

$2 y^{4} z^{2} - 6 y^{3} z + 2 y^{4} z^{2} - y^{3} z - (6 y^{4} z^{2} - y^{3} z)$

Step 2

Factor

$2 y^{3} z$ out of

$2 y^{4} z^{2} - 6 y^{3} z$ .

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Step 2.1

Factor

$2 y^{3} z$ out of

$2 y^{4} z^{2}$ .

$2 y^{3} z (y z) - 6 y^{3} z + 2 y^{4} z^{2} - y^{3} z - (6 y^{4} z^{2} - y^{3} z)$

Step 2.2

Factor

$2 y^{3} z$ out of

$- 6 y^{3} z$ .

$2 y^{3} z (y z) + 2 y^{3} z (- 3) + 2 y^{4} z^{2} - y^{3} z - (6 y^{4} z^{2} - y^{3} z)$

Step 2.3

Factor

$2 y^{3} z$ out of

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

$2 y^{3} z (y z - 3) + 2 y^{4} z^{2} - y^{3} z - (6 y^{4} z^{2} - y^{3} z)$

Step 3

Apply the distributive property.

$2 y^{3} z (y z - 3) + 2 y^{4} z^{2} - y^{3} z - (6 y^{4} z^{2}) - (- y^{3} z)$

Step 4

Multiply

$6$ by

$- 1$ .

$2 y^{3} z (y z - 3) + 2 y^{4} z^{2} - y^{3} z - 6 (y^{4} z^{2}) - (- y^{3} z)$

Step 5

Multiply

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

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Step 5.1

Multiply

$- 1$ by

$- 1$ .

$2 y^{3} z (y z - 3) + 2 y^{4} z^{2} - y^{3} z - 6 (y^{4} z^{2}) + 1 (y^{3} z)$

Step 5.2

Multiply

$y^{3}$ by

$1$ .

$2 y^{3} z (y z - 3) + 2 y^{4} z^{2} - y^{3} z - 6 (y^{4} z^{2}) + y^{3} z$

Step 6

Remove parentheses.

$2 y^{3} z (y z - 3) + 2 y^{4} z^{2} - y^{3} z - 6 y^{4} z^{2} + y^{3} z$

Step 7

Subtract

$6 y^{4} z^{2}$ from

$2 y^{4} z^{2}$ .

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

Step 8

Add

$- y^{3} z$ and

$y^{3} z$ .

$2 y^{3} z (y z - 3) - 4 y^{4} z^{2} + 0$

Step 9

Add

$- 4 y^{4} z^{2}$ and

$0$ .

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

Step 10

Factor

$2 y^{3} z$ out of

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

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Step 10.1

Factor

$2 y^{3} z$ out of

$- 4 y^{4} z^{2}$ .

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

Step 10.2

Factor

$2 y^{3} z$ out of

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

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

Step 11

Subtract

$2 y z$ from

$y z$ .

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

Step 12

Factor.

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Step 12.1

Factor

$- 1$ out of

$- y z - 3$ .

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Step 12.1.1

Factor

$- 1$ out of

$- y z$ .

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

Step 12.1.2

Rewrite

$- 3$ as

$- 1 (3)$ .

$2 y^{3} z (- (y z) - 1 (3))$

Step 12.1.3

Factor

$- 1$ out of

$- (y z) - 1 (3)$ .

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

Step 12.2

Remove unnecessary parentheses.

$2 y^{3} z \cdot - 1 (y z + 3)$

Step 13

Combine exponents.

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Step 13.1

Factor out negative.

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

Step 13.2

Multiply

$2$ by

$- 1$ .

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

Step 14

Remove unnecessary parentheses.

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