# Week 6 : Perfect square trinomials – The quadratic formula

First : Perfect Square Trinomials

We have already discussed perfect square trinomials:

$(a+b)^2= a^2+2ab+b^2$
$(a-b)^2= a^2-2ab+b^2$

We know : $a^2$ : Square of first term of binomial
2ab : twice the product of binomial’s first and last terms
$b^2$ : Square of last term of binomial

Factor : $x^2+12x+36$

Like my way, i always try the last term the numbers multiply together to get it like this :

36×1
18×2
12×3
9×4
6×6

I will choose 6×6 because if they multiply together, i will get 36 and when they add together, i will get 12 like the exercise i gave above.

You can do it faster than my way with perfect square.

Answer: (x+6)(x+6) or $(x+6)$

Example 2 : $9x^2-6x+1$

The leading coefficient is not 1 ($x^2$). Its 9 but Both $9x^2$ and 1 are perfect squares, and 6x is twice the product of 3x and 1.

So we will know a = 3a and b = 1.

Then get the answer : $(3x-1)^2$ or (3x-1)(3x-1)

Quadratic Formula : We will use this formula when we can not use Factoring and Binomial with complicated exercise. This formula will help us get answer easier and faster.

$x(1) = (-b+-(b^2-4ac)\div(2a)$
And now let’s start :

$2x^2+6x+9=0$

We knew : a=2
b=6
c=9

We will apply this formula :