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

Math
8n2+22nm+5m2
For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=5⋅8=40 and whose sum is b=22.
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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
Factor out the greatest common factor from each group.
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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

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