Solve =4b^2-8b+4-9

$$= 4 b ^ { 2 } - 8 b + 4 - 9$$

Factor

$$\left(2b-5\right)\left(2b+1\right)$$

Solution Steps

Multiply and combine like terms.

$$4b^{2}-8b-5$$

Factor the expression by grouping. First, the expression needs to be rewritten as 4b^{2}+pb+qb-5. To find p and q, set up a system to be solved.

$$p+q=-8 pq=4\left(-5\right)=-20$$

Since pq is negative, p and q have the opposite signs. Since p+q is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -20.

$$1,-20 2,-10 4,-5$$

Calculate the sum for each pair.

$$1-20=-19 2-10=-8 4-5=-1$$

The solution is the pair that gives sum -8.

$$p=-10 q=2$$

Rewrite 4b^{2}-8b-5 as \left(4b^{2}-10b\right)+\left(2b-5\right).

$$\left(4b^{2}-10b\right)+\left(2b-5\right)$$

Factor out 2b in 4b^{2}-10b.

$$2b\left(2b-5\right)+2b-5$$

Factor out common term 2b-5 by using distributive property.

$$\left(2b-5\right)\left(2b+1\right)$$

Evaluate

$$\left(2b-5\right)\left(2b+1\right)$$

Solution Steps

Subtract 9 from 4 to get -5.

$$4b^{2}-8b-5$$