4c^2 - 12c + 9
This is what I got:
(2c+3)(2c-3)
*Is that correct.?
No, it is (2c-3)^2.
To determine the correct factorization of the expression 4c^2 - 12c + 9, we can use the concept of perfect square trinomials.
A perfect square trinomial is a trinomial of the form a^2 - 2ab + b^2, where a and b are terms. In our case, the trinomial appears to follow this form.
The first step is to check if the given expression is indeed a perfect square trinomial. To do this, we compare the coefficients of the first term (4c^2), third term (9), and the middle term (-12c) with the formula for a perfect square trinomial.
In our expression, the coefficient of the first term is 4, the coefficient of the middle term is -12, and the coefficient of the third term is 9. Let's calculate (2 * sqrt(4c^2) * sqrt(9)). This evaluates to 2 * 2c * 3 = 12c, which matches the coefficient of the middle term. So, the given expression is a perfect square trinomial.
Next, we use the formula (a - b)^2 = a^2 - 2ab + b^2 to factor the expression. In our case, since the coefficient of the middle term is negative (-12c), we can rewrite it as (2c - 3)^2.
Therefore, the correct factorization of the expression 4c^2 - 12c + 9 is (2c - 3)^2.
So, your previous answer of (2c + 3)(2c - 3) was not correct.