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u^{2}+10u+16
Multiply and combine like terms.
a+b=10 ab=1\times 16=16
Factor the expression by grouping. First, the expression needs to be rewritten as u^{2}+au+bu+16. To find a and b, set up a system to be solved.
1,16 2,8 4,4
Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 16.
1+16=17 2+8=10 4+4=8
Calculate the sum for each pair.
a=2 b=8
The solution is the pair that gives sum 10.
\left(u^{2}+2u\right)+\left(8u+16\right)
Rewrite u^{2}+10u+16 as \left(u^{2}+2u\right)+\left(8u+16\right).
u\left(u+2\right)+8\left(u+2\right)
Factor out u in the first and 8 in the second group.
\left(u+2\right)\left(u+8\right)
Factor out common term u+2 by using distributive property.
u^{2}+10u+16
Combine 2u and 8u to get 10u.