help!!! i don't know how to factorize 9x*squared* - 12x +4! HELLLPPPPPP!
hint: perfect square
9x2 -12x + 4
What is 2*2*3? ahha!
(3x-2)(3x-2) How did I arrive at that? I know the center term is always 2ab in
a perfect square, such as (ax+b)^2 Memorize that.
Of course, I can help you factorize the quadratic expression. To factorize 9x^2 - 12x + 4, first, look for a pair of numbers that multiply to give you the product of the first and last terms, which are 9x^2 and 4, respectively.
In this case, the product of 9x^2 and 4 is 36x^2. Now, we need to find a pair of numbers that add up to give the coefficient of the middle term, which is -12x.
Let's break it down step-by-step:
Step 1: Multiply the coefficient of the first term (9x^2) by the constant term (4).
9x^2 * 4 = 36x^2
Step 2: Now, we need to find two numbers that multiply to give 36x^2 and add to give -12x. The numbers that fit this criteria are -6x and -6x.
Step 3: Rewrite the middle term (-12x) using the two numbers found in Step 2.
-6x - 6x = -12x
Step 4: Now, we can factor using grouping or split the middle term method.
Split the middle term method:
Step 5: Rewrite the expression with four terms, replacing the middle term (-12x) with the two terms found in Step 2.
9x^2 - 6x - 6x + 4
Step 6: Group the terms into pairs and factor out the greatest common factor from each pair.
(9x^2 - 6x) - (6x - 4)
Step 7: Factor out the GCF from each pair.
3x(3x - 2) - 2(3x - 2)
Step 8: Notice that the terms in the parentheses are now the same.
(3x - 2)(3x - 2)
Step 9: Finally, the expression 9x^2 - 12x + 4 is factored as (3x - 2)(3x - 2), or simply (3x - 2)^2.
So, the factored form of 9x^2 - 12x + 4 is (3x - 2)^2.