Algebra Examples

$150 m^{2} n z + 20 m n^{2} c - 120 m^{2} n c - 25 m n^{2} z$

Step 1

Factor $5 m n$ out of $150 m^{2} n z + 20 m n^{2} c - 120 m^{2} n c - 25 m n^{2} z$ .

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Step 1.1

Factor $5 m n$ out of $150 m^{2} n z$ .

$5 m n (30 m z) + 20 m n^{2} c - 120 m^{2} n c - 25 m n^{2} z$

Step 1.2

Factor $5 m n$ out of $20 m n^{2} c$ .

$5 m n (30 m z) + 5 m n (4 n c) - 120 m^{2} n c - 25 m n^{2} z$

Step 1.3

Factor $5 m n$ out of $- 120 m^{2} n c$ .

$5 m n (30 m z) + 5 m n (4 n c) + 5 m n (- 24 m c) - 25 m n^{2} z$

Step 1.4

Factor $5 m n$ out of $- 25 m n^{2} z$ .

$5 m n (30 m z) + 5 m n (4 n c) + 5 m n (- 24 m c) + 5 m n (- 5 n z)$

Step 1.5

Factor $5 m n$ out of $5 m n (30 m z) + 5 m n (4 n c)$ .

$5 m n (30 m z + 4 n c) + 5 m n (- 24 m c) + 5 m n (- 5 n z)$

Step 1.6

Factor $5 m n$ out of $5 m n (30 m z + 4 n c) + 5 m n (- 24 m c)$ .

$5 m n (30 m z + 4 n c - 24 m c) + 5 m n (- 5 n z)$

Step 1.7

Factor $5 m n$ out of $5 m n (30 m z + 4 n c - 24 m c) + 5 m n (- 5 n z)$ .

$5 m n (30 m z + 4 n c - 24 m c - 5 n z)$

Step 2

Regroup terms.

$5 m n (- 24 m c + 30 m z + 4 n c - 5 n z)$

Step 3

Factor out the greatest common factor from each group.

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Step 3.1

Group the first two terms and the last two terms.

$5 m n ((- 24 m c + 30 m z) + 4 n c - 5 n z)$

Step 3.2

Factor out the greatest common factor (GCF) from each group.

$5 m n (6 m (- 4 c + 5 z) - n (- 4 c + 5 z))$

Step 4

Factor.

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Step 4.1

Factor the polynomial by factoring out the greatest common factor, $- 4 c + 5 z$ .

$5 m n ((- 4 c + 5 z) (6 m - n))$

Step 4.2

Remove unnecessary parentheses.

$5 m n (- 4 c + 5 z) (6 m - n)$

Step 5

Factor.

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Step 5.1

Factor $- 1$ out of $- 4 c + 5 z$ .

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Step 5.1.1

Factor $- 1$ out of $- 4 c$ .

$5 m n (- (4 c) + 5 z) (6 m - n)$

Step 5.1.2

Factor $- 1$ out of $5 z$ .

$5 m n (- (4 c) - (- 5 z)) (6 m - n)$

Step 5.1.3

Factor $- 1$ out of $- (4 c) - (- 5 z)$ .

$5 m n (- (4 c - 5 z)) (6 m - n)$

Step 5.2

Remove unnecessary parentheses.

$5 m n \cdot - 1 (4 c - 5 z) (6 m - n)$

Step 6

Factor.

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Step 6.1

Combine exponents.

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Step 6.1.1

Factor out negative.

$- ((5 m n (4 c - 5 z)) (6 m - n))$

Step 6.1.2

Multiply $5$ by $- 1$ .

$- 5 ((m n (4 c - 5 z)) (6 m - n))$

Step 6.2

Remove unnecessary parentheses.

$- 5 m n (4 c - 5 z) (6 m - n)$