I really need help factoring these special Trinomials.
This question really puzzled me. I thought I had it correct, but when I checked the answer at the back of the book, I was wrong, and so I would like to know what was it that I had done wrong.
This was the question:
x^2-4x+4
This is how I solved it:
x^2-4x+4
x^2-2x-2x+4
x(x-2)-2(x+2)
(x-2)(x+2)
- I could not get any further than this. I thought that this would be correct, but the actual answer is
(x-2)^2
How did they get that?
If there is an easier way to solve this, then can you please show me how. Cause solving things like I have above is difficult.
see
http://www.jiskha.com/display.cgi?id=1289262952
To factor the trinomial x^2-4x+4, you were on the right track initially by breaking down the term -4x into -2x and -2x. Then, you factored the common terms from each binomial to get x(x-2)-2(x+2). However, there was a small error in the next step.
Let's correct that and find the correct factored form:
x(x-2)-2(x+2)
Now, distribute the -2 to both terms inside the second parentheses:
x(x-2)-2x-4
Combine like terms:
x^2 - 2x - 2x - 4
Now, simplify further:
x^2 - 4x - 4
To find the correct factored form, we need to look for a perfect square trinomial. In this case, the first and last terms are both perfect squares: x^2 is (x^2)^1/2, and -4 is (-2)^2.
The perfect square trinomial can be factored into the square of a binomial. Here's how:
Start with the first term: x^2
This can be factored as (x)^2
Next, take the square root of the middle term -4, which is -2.
Now, write the factored form using the square of a binomial pattern:
(x - 2)^2
So, the correct factored form of the trinomial x^2-4x+4 is (x - 2)^2.
Alternatively, if you prefer an easier method to factor a perfect square trinomial like this, you can use the formula:
a^2 - 2ab + b^2 = (a - b)^2
In this case, a = x and b = 2. Plugging in these values into the formula, we get:
x^2 - 2(x)(2) + 2^2 = (x - 2)^2
So, using the formula, we can directly write the factored form as (x - 2)^2.
I hope this explanation helps you understand the correct solution and the easier method of factoring perfect square trinomials.