How to factor PST
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Answers & Comments
Answer:
One good way to recognize if a trinomial is perfect square is to look at its first and third term. If they are both squares, there's a good chance that you may be working with a perfect square trinomial.
Let's say we're working with the following: x^{2}+14x+49x
2
+14x+49. Is this a perfect square trinomial? Looking at the first term, we've got x^{2}x
2
, which is a square. The last term is 4949. It is also a square since when you multiply 77 by 77, you'll get 4949. Therefore 4949 can also be written as 7^{2}7
2
. The next step to identifying if we've got a perfect square is to see if we are able to get the middle term of 14x14x when we have x^{2}x
2
and 7^{2}7
2
to work with.
In the case of a perfect square, the middle term is the first term multiplied by the last term, and then multiplied by 22. In other words, the perfect square trinomial formula is:
a^{2} \pm ab + b^{2}a
2
±ab+b
2
. We're now trying to see if we can get the middle term of 2ab2ab.
Since we've got our aa term as xx, and our bb term as 77, our 2ab2ab becomes 2 \bullet 7 \bullet x2∙7∙x. That gives us a total of 14x14x, which is the middle term in x^{2}+14x+49x
2
+14x+49! Therefore, we can rewrite the question as (x + 7)^{2}(x+7)
2
through factoring perfect square trinomials. You've solved a perfect square trinomial! You're now ready to apply trinomial factoring to some practice problems.