Solve 8x^2+40x+5x+25

$$8 x ^ { 2 } + 40 x + 5 x + 25$$

Factor

$$\left(x+5\right)\left(8x+5\right)$$

Solution Steps

Multiply and combine like terms.

$$8x^{2}+45x+25$$

Factor the expression by grouping. First, the expression needs to be rewritten as 8x^{2}+ax+bx+25. To find a and b, set up a system to be solved.

$$a+b=45 ab=8\times 25=200$$

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 200.

$$1,200 2,100 4,50 5,40 8,25 10,20$$

Calculate the sum for each pair.

$$1+200=201 2+100=102 4+50=54 5+40=45 8+25=33 10+20=30$$

The solution is the pair that gives sum 45.

$$a=5 b=40$$

Rewrite 8x^{2}+45x+25 as \left(8x^{2}+5x\right)+\left(40x+25\right).

$$\left(8x^{2}+5x\right)+\left(40x+25\right)$$

Factor out x in the first and 5 in the second group.

$$x\left(8x+5\right)+5\left(8x+5\right)$$

Factor out common term 8x+5 by using distributive property.

$$\left(8x+5\right)\left(x+5\right)$$

Evaluate

$$\left(x+5\right)\left(8x+5\right)$$

Solution Steps

Combine 40x and 5x to get 45x.

$$8x^{2}+45x+25$$