Solve (3s^2+3s)+(7s+7)

$$( 3 s ^ { 2 } + 3 s ) + ( 7 s + 7 )$$

Factor

$$\left(s+1\right)\left(3s+7\right)$$

Solution Steps

Multiply and combine like terms.

$$3s^{2}+10s+7$$

Factor the expression by grouping. First, the expression needs to be rewritten as 3s^{2}+as+bs+7. To find a and b, set up a system to be solved.

$$a+b=10 ab=3\times 7=21$$

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 21.

$$1,21 3,7$$

Calculate the sum for each pair.

$$1+21=22 3+7=10$$

The solution is the pair that gives sum 10.

$$a=3 b=7$$

Rewrite 3s^{2}+10s+7 as \left(3s^{2}+3s\right)+\left(7s+7\right).

$$\left(3s^{2}+3s\right)+\left(7s+7\right)$$

Factor out 3s in the first and 7 in the second group.

$$3s\left(s+1\right)+7\left(s+1\right)$$

Factor out common term s+1 by using distributive property.

$$\left(s+1\right)\left(3s+7\right)$$

Evaluate

$$\left(s+1\right)\left(3s+7\right)$$

Solution Steps

Combine 3s and 7s to get 10s.

$$3s^{2}+10s+7$$