Algebra Help Please?

Question

I need to use a special product formula to factor the perfect square trinomial of 9x^2 -12x + 4, I think the answer is (2x - 2)^2 but I am unsure can you help?

Answer 1

9x² - 12x + 4
First of all you require two numbers that multiply to give 9x²
Such numbers are 3x and 3x or 9x and x.
Try 3x and 3x:-
(3x-------).(3x-------)
Now require two numbers that multiply to give 4 and combine to give - 12x:-
Such numbers are - 2 and -2 :-
(3x - 2).(3x - 2) = (3x - 2)² is answer
Check
3x.(3x - 2) - 2.(3x - 2)
= 9x² - 6x - 6x + 4
= 9x² - 12x + 4 (as required)

Answer 2

The special product formula looks like this:

A^2 + 2AB + B^2

So once your trinomial is in descending order by one variable (and yours is, in the variable x) you look at the square roots of the outer terms:

For your trinomial 9x^2 -12x + 4 your square roots would be

3x and 2 (where either or both terms could be negative, since the square of a negative is equal to the square of a positive); then you check the middle term of your trinomial and see if NUMERICALLY it's equal to twice the product of the 2 roots. [It is: 2(3x)(2) = 12x.]

Now you make an accomodation for the middle term's sign by making one of the terms [either 3x or 2] negative.

So your possible factoring could be either

A) [3x - 2] squared which is [-2 + 3x] squared OR

B) [-(3x) + 2] squared which is [2 - 3x] squared

Answer 3

(3x - 2)²

The square of your first term should be 9x², which squaring 3x will give you. Multiply out using FOIL to verify:

(3x)(3x) + (-2)(3x) + (-2)(3x) + (-2)(-2)

= 9x² - 12x + 4

Answer 4

It's (3x-2)^2 because 3x X3x=9x^2

Answer 5

9x^2-12x+4=(3x)^2-2*3x*2+(2)^2=(3x-2)^2

Answer 6

(3x-2)^2