Factor 18x^3y-51x^2y^2-42xy^3

$18 x^{3} y - 51 x^{2} y^{2} - 42 x y^{3}$

Step 1

Factor $3 x y$ out of $18 x^{3} y - 51 x^{2} y^{2} - 42 x y^{3}$ .

Factor $3 x y$ out of $18 x^{3} y$ .

$3 x y (6 x^{2}) - 51 x^{2} y^{2} - 42 x y^{3}$

Factor $3 x y$ out of $- 51 x^{2} y^{2}$ .

$3 x y (6 x^{2}) + 3 x y (- 17 x y) - 42 x y^{3}$

Factor $3 x y$ out of $- 42 x y^{3}$ .

$3 x y (6 x^{2}) + 3 x y (- 17 x y) + 3 x y (- 14 y^{2})$

Factor $3 x y$ out of $3 x y (6 x^{2}) + 3 x y (- 17 x y)$ .

$3 x y (6 x^{2} - 17 x y) + 3 x y (- 14 y^{2})$

Factor $3 x y$ out of $3 x y (6 x^{2} - 17 x y) + 3 x y (- 14 y^{2})$ .

$3 x y (6 x^{2} - 17 x y - 14 y^{2})$

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 $a \cdot c = 6 \cdot - 14 = - 84$ and whose sum is $b = - 17$ .

Reorder terms.

$3 x y (6 x^{2} - 14 y^{2} - 17 x y)$

Reorder $- 14 y^{2}$ and $- 17 x y$ .

$3 x y (6 x^{2} - 17 x y - 14 y^{2})$

Factor $- 17$ out of $- 17 x y$ .

$3 x y (6 x^{2} - 17 (x y) - 14 y^{2})$

Rewrite $- 17$ as $4$ plus $- 21$

$3 x y (6 x^{2} + (4 - 21) (x y) - 14 y^{2})$

Apply the distributive property.

$3 x y (6 x^{2} + 4 (x y) - 21 (x y) - 14 y^{2})$

Remove unnecessary parentheses.

$3 x y (6 x^{2} + 4 x y - 21 (x y) - 14 y^{2})$

Remove unnecessary parentheses.

$3 x y (6 x^{2} + 4 x y - 21 x y - 14 y^{2})$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$3 x y ((6 x^{2} + 4 x y) - 21 x y - 14 y^{2})$

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

$3 x y (2 x (3 x + 2 y) - 7 y (3 x + 2 y))$

Factor the polynomial by factoring out the greatest common factor, $3 x + 2 y$ .

$3 x y ((3 x + 2 y) (2 x - 7 y))$

Remove unnecessary parentheses.

$3 x y (3 x + 2 y) (2 x - 7 y)$

Factor 18x^3y-51x^2y^2-42xy^3

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