In Exercises 49–56, factor each perfect square trinomial. 64x^2−1...

Question

In Exercises 49–56, factor each perfect square trinomial. 64x^2−16x+1

Accepted Answer

Hello. Today we're gonna be factoring a given try no meal. So the tri no meal given to us is 16 X squared minus 24 X plus nine. Now when we factor this this is going to factor into two mono meals that have a combination of terms that are factors of the first term of our try no meal and the last term of our try no meal. So the first term is 16 X squared but this is a perfect square because it could be rewritten as four X squared and the last term nine is a perfect square because it could be rewritten as three squared. So this try no meal is going to have to factor two to mono meals that have the terms four X and three in them. Now we need to decide if these are being added or subtracted from each other. Well we have the signs plus and minus. So that tells us that both these quantities are going to have to be differences. Now we need to go ahead and verify that this gives us the original try no meal 16 X squared minus 24 x plus nine. So if we factor it together we're gonna see if we get this try no meal. So four x times four X gives us 16 X squared four x times negative three, gives us negative 12 X negative three times four X gives us negative 12 X and negative three times negative three gives us positive nine. When we combine our like terms which is the negative 12 X and negative 12 x. We get 16 X squared minus 24 X plus nine and this verifies that. This is going to be the factor of our original try no meal. Now if you notice both of these quantities are the same quantity four x minus three and four x minus three so we can go ahead and combine them into a single mono meal and rewrite it as four x minus three squared. And this is going to be the factored version of our given try no meal and the answer to this problem is going to be C. So I hope this video helps you in understanding how to factor this trin Amiel and I'll go ahead and see you all in the next video.

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