Factor 6x^2y-62xy+72y

$6 x^{2} y - 62 x y + 72 y$

Step 1

Factor $2 y$ out of $6 x^{2} y - 62 x y + 72 y$ .

Factor $2 y$ out of $6 x^{2} y$ .

$2 y (3 x^{2}) - 62 x y + 72 y$

Factor $2 y$ out of $- 62 x y$ .

$2 y (3 x^{2}) + 2 y (- 31 x) + 72 y$

Factor $2 y$ out of $72 y$ .

$2 y (3 x^{2}) + 2 y (- 31 x) + 2 y (36)$

Factor $2 y$ out of $2 y (3 x^{2}) + 2 y (- 31 x)$ .

$2 y (3 x^{2} - 31 x) + 2 y (36)$

Factor $2 y$ out of $2 y (3 x^{2} - 31 x) + 2 y (36)$ .

$2 y (3 x^{2} - 31 x + 36)$

Step 2

Factor.

Factor by grouping.

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 $a \cdot c = 3 \cdot 36 = 108$ and whose sum is $b = - 31$ .

Factor $- 31$ out of $- 31 x$ .

$2 y (3 x^{2} - 31 (x) + 36)$

Rewrite $- 31$ as $- 4$ plus $- 27$

$2 y (3 x^{2} + (- 4 - 27) x + 36)$

Apply the distributive property.

$2 y (3 x^{2} - 4 x - 27 x + 36)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 y ((3 x^{2} - 4 x) - 27 x + 36)$

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

$2 y (x (3 x - 4) - 9 (3 x - 4))$

Factor the polynomial by factoring out the greatest common factor, $3 x - 4$ .

$2 y ((3 x - 4) (x - 9))$

Remove unnecessary parentheses.

$2 y (3 x - 4) (x - 9)$

Factor 6x^2y-62xy+72y

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