Factor x^2-7xy+12y^2

$x^{2} - 7 x y + 12 y^{2}$

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 $a \cdot c = 1 \cdot 12 = 12$ and whose sum is $b = - 7$ .

Reorder terms.

$x^{2} + 12 y^{2} - 7 x y$

Reorder $12 y^{2}$ and $- 7 x y$ .

$x^{2} - 7 x y + 12 y^{2}$

Factor $- 7$ out of $- 7 x y$ .

$x^{2} - 7 (x y) + 12 y^{2}$

Rewrite $- 7$ as $- 3$ plus $- 4$

$x^{2} + (- 3 - 4) (x y) + 12 y^{2}$

Apply the distributive property.

$x^{2} - 3 (x y) - 4 (x y) + 12 y^{2}$

Remove unnecessary parentheses.

$x^{2} - 3 x y - 4 (x y) + 12 y^{2}$

Remove unnecessary parentheses.

$x^{2} - 3 x y - 4 x y + 12 y^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{2} - 3 x y) - 4 x y + 12 y^{2}$

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

$x (x - 3 y) - 4 y (x - 3 y)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $x - 3 y$ .

$(x - 3 y) (x - 4 y)$

Factor x^2-7xy+12y^2

Related Questions

Support LCMGCF.com by disabling your adblocker.