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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:


This is how I solved it:


- I could not get any further than this. I thought that this would be correct, but the actual answer is

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.

  • MATH-STUCK :-( -

    Your error is in this line of yours

    notice when you multiply it back out you don't get your original, and you don't have a "common" factor.

    should have been
    x(x-2)-2(x-2) to get back your x^2 - 4x + 4
    = (x-2)(x-2)
    = (x-2)^2

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