8n2+22nm+5m2

Reorder terms.

5m2+8n2+22mn

Reorder 8n2 and 22mn.

5m2+22mn+8n2

Factor 22 out of 22mn.

5m2+22(mn)+8n2

Rewrite 22 as 2 plus 20

5m2+(2+20)(mn)+8n2

Apply the distributive property.

5m2+2(mn)+20(mn)+8n2

Remove unnecessary parentheses.

5m2+2mn+20(mn)+8n2

Remove unnecessary parentheses.

5m2+2mn+20mn+8n2

5m2+2mn+20mn+8n2

Group the first two terms and the last two terms.

(5m2+2mn)+20mn+8n2

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

m(5m+2n)+4n(5m+2n)

m(5m+2n)+4n(5m+2n)

Factor the polynomial by factoring out the greatest common factor, 5m+2n.

(5m+2n)(m+4n)

Factor 8n^2+22nm+5m^2