Factor 14x^2y^2+5xy-24

$14 x^{2} y^{2} + 5 x y - 24$

Step 1

Rewrite $x^{2} y^{2}$ as ${(x y)}^{2}$ .

$14 {(x y)}^{2} + 5 (x y) - 24$

Step 2

Let $u = x y$ . Substitute $u$ for all occurrences of $x y$ .

$14 u^{2} + 5 u - 24$

Step 3

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 $a \cdot c = 14 \cdot - 24 = - 336$ and whose sum is $b = 5$ .

Factor $5$ out of $5 u$ .

$14 u^{2} + 5 (u) - 24$

Rewrite $5$ as $- 16$ plus $21$

$14 u^{2} + (- 16 + 21) u - 24$

Apply the distributive property.

$14 u^{2} - 16 u + 21 u - 24$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(14 u^{2} - 16 u) + 21 u - 24$

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

$2 u (7 u - 8) + 3 (7 u - 8)$

Factor the polynomial by factoring out the greatest common factor, $7 u - 8$ .

$(7 u - 8) (2 u + 3)$

Step 4

Replace all occurrences of $u$ with $x y$ .

$(7 (x y) - 8) (2 (x y) + 3)$

Step 5

Simplify.

Remove parentheses.

$(7 x y - 8) (2 (x y) + 3)$

Remove parentheses.

$(7 x y - 8) (2 x y + 3)$

Factor 14x^2y^2+5xy-24

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