Solve 4x^2-6x-6x+9

$$4 x ^ { 2 } - 6 x - 6 x + 9$$

Factor

$$\left(2x-3\right)^{2}$$

Solution Steps

Multiply and combine like terms.

$$4x^{2}-12x+9$$

Factor the expression by grouping. First, the expression needs to be rewritten as 4x^{2}+ax+bx+9. To find a and b, set up a system to be solved.

$$a+b=-12 ab=4\times 9=36$$

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 36.

$$-1,-36 -2,-18 -3,-12 -4,-9 -6,-6$$

Calculate the sum for each pair.

$$-1-36=-37 -2-18=-20 -3-12=-15 -4-9=-13 -6-6=-12$$

The solution is the pair that gives sum -12.

$$a=-6 b=-6$$

Rewrite 4x^{2}-12x+9 as \left(4x^{2}-6x\right)+\left(-6x+9\right).

$$\left(4x^{2}-6x\right)+\left(-6x+9\right)$$

Factor out 2x in the first and -3 in the second group.

$$2x\left(2x-3\right)-3\left(2x-3\right)$$

Factor out common term 2x-3 by using distributive property.

$$\left(2x-3\right)\left(2x-3\right)$$

Rewrite as a binomial square.

$$\left(2x-3\right)^{2}$$

Evaluate

$$\left(2x-3\right)^{2}$$

Solution Steps

Combine -6x and -6x to get -12x.

$$4x^{2}-12x+9$$