Factor 10m^2+7mn-12n^2

$10 m^{2} + 7 m n - 12 n^{2}$

Step 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 $a \cdot c = 10 \cdot - 12 = - 120$ and whose sum is $b = 7$ .

Reorder terms.

$10 m^{2} - 12 n^{2} + 7 m n$

Reorder $- 12 n^{2}$ and $7 m n$ .

$10 m^{2} + 7 m n - 12 n^{2}$

Factor $7$ out of $7 m n$ .

$10 m^{2} + 7 (m n) - 12 n^{2}$

Rewrite $7$ as $- 8$ plus $15$

$10 m^{2} + (- 8 + 15) (m n) - 12 n^{2}$

Apply the distributive property.

$10 m^{2} - 8 (m n) + 15 (m n) - 12 n^{2}$

Remove unnecessary parentheses.

$10 m^{2} - 8 m n + 15 (m n) - 12 n^{2}$

Remove unnecessary parentheses.

$10 m^{2} - 8 m n + 15 m n - 12 n^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 m^{2} - 8 m n) + 15 m n - 12 n^{2}$

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

$2 m (5 m - 4 n) + 3 n (5 m - 4 n)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 m - 4 n$ .

$(5 m - 4 n) (2 m + 3 n)$

Factor 10m^2+7mn-12n^2

Related Questions

Support LCMGCF.com by disabling your adblocker.