Solve b^2+5b+3b+16

$$b ^ { 2 } + 5 b + 3 b + 16$$

Factor

$$\left(b+4\right)^{2}$$

Solution Steps

Multiply and combine like terms.

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

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

$$p+q=8 pq=1\times 16=16$$

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 8.

$$p=4 q=4$$

Rewrite b^{2}+8b+16 as \left(b^{2}+4b\right)+\left(4b+16\right).

$$\left(b^{2}+4b\right)+\left(4b+16\right)$$

Factor out b in the first and 4 in the second group.

$$b\left(b+4\right)+4\left(b+4\right)$$

Factor out common term b+4 by using distributive property.

$$\left(b+4\right)\left(b+4\right)$$

Rewrite as a binomial square.

$$\left(b+4\right)^{2}$$

Evaluate

$$\left(b+4\right)^{2}$$

Solution Steps

Combine 5b and 3b to get 8b.

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