Algebra Examples

$5 n^{2} - 11 m n + 6 m^{2}$ entre $m - n$

Step 1

Write the problem as a mathematical expression.

$\frac{5 n^{2} - 11 m n + 6 m^{2}}{m - n}$

Step 2

Factor by grouping.

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Step 2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 6 \cdot 5 = 30$ and whose sum is $b = - 11$ .

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Step 2.1.1

Reorder terms.

$\frac{6 m^{2} + 5 n^{2} - 11 m n}{m - n}$

Step 2.1.2

Reorder $5 n^{2}$ and $- 11 m n$ .

$\frac{6 m^{2} - 11 m n + 5 n^{2}}{m - n}$

Step 2.1.3

Factor $- 11$ out of $- 11 m n$ .

$\frac{6 m^{2} - 11 (m n) + 5 n^{2}}{m - n}$

Step 2.1.4

Rewrite $- 11$ as $- 5$ plus $- 6$

$\frac{6 m^{2} + (- 5 - 6) (m n) + 5 n^{2}}{m - n}$

Step 2.1.5

Apply the distributive property.

$\frac{6 m^{2} - 5 (m n) - 6 (m n) + 5 n^{2}}{m - n}$

Step 2.1.6

Move parentheses.

$\frac{6 m^{2} - 5 m n - 6 m n + 5 n^{2}}{m - n}$

Step 2.2

Factor out the greatest common factor from each group.

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Step 2.2.1

Group the first two terms and the last two terms.

$\frac{(6 m^{2} - 5 m n) - 6 m n + 5 n^{2}}{m - n}$

Step 2.2.2

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

$\frac{m (6 m - 5 n) - n (6 m - 5 n)}{m - n}$

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $6 m - 5 n$ .

$\frac{(6 m - 5 n) (m - n)}{m - n}$

Step 3

Cancel the common factor of $m - n$ .

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Step 3.1

Cancel the common factor.

$\frac{(6 m - 5 n) (m - n)}{m - n}$

Step 3.2

Divide $6 m - 5 n$ by $1$ .

$6 m - 5 n$