Factor 4x^2y-13xy+9y

$4 x^{2} y - 13 x y + 9 y$

Step 1

Factor $y$ out of $4 x^{2} y - 13 x y + 9 y$ .

Factor $y$ out of $4 x^{2} y$ .

$y (4 x^{2}) - 13 x y + 9 y$

Factor $y$ out of $- 13 x y$ .

$y (4 x^{2}) + y (- 13 x) + 9 y$

Factor $y$ out of $9 y$ .

$y (4 x^{2}) + y (- 13 x) + y \cdot 9$

Factor $y$ out of $y (4 x^{2}) + y (- 13 x)$ .

$y (4 x^{2} - 13 x) + y \cdot 9$

Factor $y$ out of $y (4 x^{2} - 13 x) + y \cdot 9$ .

$y (4 x^{2} - 13 x + 9)$

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 $a \cdot c = 4 \cdot 9 = 36$ and whose sum is $b = - 13$ .

Factor $- 13$ out of $- 13 x$ .

$y (4 x^{2} - 13 (x) + 9)$

Rewrite $- 13$ as $- 4$ plus $- 9$

$y (4 x^{2} + (- 4 - 9) x + 9)$

Apply the distributive property.

$y (4 x^{2} - 4 x - 9 x + 9)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$y ((4 x^{2} - 4 x) - 9 x + 9)$

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

$y (4 x (x - 1) - 9 (x - 1))$

Factor the polynomial by factoring out the greatest common factor, $x - 1$ .

$y ((x - 1) (4 x - 9))$

Remove unnecessary parentheses.

$y (x - 1) (4 x - 9)$

Factor 4x^2y-13xy+9y

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