Solve u^2+2u+8u+16

$$u ^ { 2 } + 2 u + 8 u + 16$$

Factor

$$\left(u+2\right)\left(u+8\right)$$

Solution Steps

Multiply and combine like terms.

$$u^{2}+10u+16$$

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.

$$a+b=10 ab=1\times 16=16$$

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.

$$1,16 2,8 4,4$$

Calculate the sum for each pair.

$$1+16=17 2+8=10 4+4=8$$

The solution is the pair that gives sum 10.

$$a=2 b=8$$

Rewrite u^{2}+10u+16 as \left(u^{2}+2u\right)+\left(8u+16\right).

$$\left(u^{2}+2u\right)+\left(8u+16\right)$$

Factor out u in the first and 8 in the second group.

$$u\left(u+2\right)+8\left(u+2\right)$$

Factor out common term u+2 by using distributive property.

$$\left(u+2\right)\left(u+8\right)$$

Evaluate

$$\left(u+2\right)\left(u+8\right)$$

Solution Steps

Combine 2u and 8u to get 10u.

$$u^{2}+10u+16$$