Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$n^{2} (2 n) + n^{2} \cdot - 5 + 2 n - 5$

Step 1.2

Rewrite using the commutative property of multiplication.

$2 n^{2} n + n^{2} \cdot - 5 + 2 n - 5$

Step 1.3

Move $- 5$ to the left of $n^{2}$ .

$2 n^{2} n - 5 \cdot n^{2} + 2 n - 5$

Step 1.4

Multiply $n^{2}$ by $n$ by adding the exponents.

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Step 1.4.1

Move $n$ .

$2 (n \cdot n^{2}) - 5 \cdot n^{2} + 2 n - 5$

Step 1.4.2

Multiply $n$ by $n^{2}$ .

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Step 1.4.2.1

Raise $n$ to the power of $1$ .

$2 (n^{1} n^{2}) - 5 \cdot n^{2} + 2 n - 5$

Step 1.4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 n^{1 + 2} - 5 \cdot n^{2} + 2 n - 5$

Step 1.4.3

Add $1$ and $2$ .

$2 n^{3} - 5 \cdot n^{2} + 2 n - 5$

$2 n^{3} - 5 n^{2} + 2 n - 5$

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.

$(2 n^{3} - 5 n^{2}) + 2 n - 5$

Step 2.2

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

$n^{2} (2 n - 5) + 1 (2 n - 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 n - 5$ .

$(2 n - 5) (n^{2} + 1)$