how do i factor the perfect square trinomial 9x2-12x+4
(3 2 ) (3 2) have to appear if it is a perfect square to get that 9 and 4
it has to be - 2 times -2 to get +4 and -12
so try
(3x-2)(3x-2)
sure enough
To factor the perfect square trinomial 9x^2 - 12x + 4, follow these steps:
Step 1: Identify the perfect square pattern
A perfect square trinomial has a specific pattern: (a + b)^2 = a^2 + 2ab + b^2.
Step 2: Rewrite the trinomial using the pattern
In this case, we have 9x^2 - 12x + 4. Notice that 9x^2 is the square of 3x, and 4 is the square of 2. So, rewrite the expression using the pattern: (3x)^2 - 2(3x)(2) + (2)^2.
Step 3: Simplify the expression
Simplify the expression using the pattern: (3x - 2)^2.
Therefore, the factored form of 9x^2 - 12x + 4 is (3x - 2)^2.
To factor a perfect square trinomial, follow these steps:
Step 1: Identify if the trinomial is a perfect square trinomial. A perfect square trinomial is in the form of (ax)^2 − 2abx + b^2, where a and b are constants.
In your case, the trinomial is 9x^2 − 12x + 4. To determine if it's a perfect square trinomial, compare it with the general form: (ax)^2 − 2abx + b^2.
In the given trinomial, a^2 = 9x^2, so a = 3x.
Similarly, b^2 = 4, so b = 2.
Step 2: Write the factored form of the perfect square trinomial. It will be in the form of (ax − b)^2.
Using the values of a and b from step 1, we have:
(3x − 2)^2
Therefore, the factored form of 9x^2 − 12x + 4 is (3x − 2)^2.