21x2y2+11xy-2

Rewrite x2y2 as (xy)2.

21(xy)2+11(xy)-2

Let u=xy. Substitute u for all occurrences of xy.

21u2+11u-2

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=21⋅-2=-42 and whose sum is b=11.

Factor 11 out of 11u.

21u2+11(u)-2

Rewrite 11 as -3 plus 14

21u2+(-3+14)u-2

Apply the distributive property.

21u2-3u+14u-2

21u2-3u+14u-2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(21u2-3u)+14u-2

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

3u(7u-1)+2(7u-1)

3u(7u-1)+2(7u-1)

Factor the polynomial by factoring out the greatest common factor, 7u-1.

(7u-1)(3u+2)

(7u-1)(3u+2)

Replace all occurrences of u with xy.

(7(xy)-1)(3(xy)+2)

Remove parentheses.

(7xy-1)(3(xy)+2)

Remove parentheses.

(7xy-1)(3xy+2)

(7xy-1)(3xy+2)

Factor 21x^2y^2+11xy-2