Algebra Examples

$5 n^{2} p - 10 n p - 5 n^{2} + 10 n$

Step 1

Factor out the GCF of $5 n$ from $5 n^{2} p - 10 n p - 5 n^{2} + 10 n$ .

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Step 1.1

Factor out the GCF of $5 n$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $5 n$ from the expression $5 n^{2} p$ .

$5 n (n p) - 10 n p - 5 n^{2} + 10 n$

Step 1.1.2

Factor out the GCF of $5 n$ from the expression $- 10 n p$ .

$5 n (n p) + 5 n (- 2 p) - 5 n^{2} + 10 n$

Step 1.1.3

Factor out the GCF of $5 n$ from the expression $- 5 n^{2}$ .

$5 n (n p) + 5 n (- 2 p) + 5 n (- n) + 10 n$

Step 1.1.4

Factor out the GCF of $5 n$ from the expression $10 n$ .

$5 n (n p) + 5 n (- 2 p) + 5 n (- n) + 5 n (2)$

Step 1.2

Since all the terms share a common factor of $5 n$ , it can be factored out of each term.

$5 n (n p - 2 p - n + 2)$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$5 n ((n p - 2 p) - n + 2)$

Step 2.2

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

$5 n (p (n - 2) - (n - 2))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $n - 2$ .

$5 n ((n - 2) (p - 1))$