Solve a^2+2a+8a+16

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

Factor

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

Solution Steps

Multiply and combine like terms.

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

Factor the expression by grouping. First, the expression needs to be rewritten as a^{2}+pa+qa+16. To find p and q, set up a system to be solved.

$$p+q=10 pq=1\times 16=16$$

Since pq is positive, p and q have the same sign. Since p+q is positive, p and q 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.

$$p=2 q=8$$

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

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

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

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

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

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

Evaluate

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

Solution Steps

Combine 2a and 8a to get 10a.

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