SOLUTION: Factor the expression Chapter 5 Algebra II X4-50x2+625 Please help me with example to solve the above. Thank You.. Aaron

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Question 182268: Factor the expression Chapter 5 Algebra II
X4-50x2+625
Please help me with example to solve the above.
Thank You.. Aaron
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
X%5E4-50x%5E2%2B625

First notice that 625 just happens to be the square of 25. So, try to factor this as a binomial times a binomial. The x^4 breaks down into x^2 * x^2 like this:
%28x%5E2+-+____%29%28x%5E2+-+_____%29

Now try the 25*25. It goes like this:
%28x%5E2+-+25%29%28x%5E2+-+25%29

Each of these is a difference of two squares, which factor again.
+%28x-5%29%28x%2B5%29%28x-5%29%28x%2B5%29+, which can also be written +%28x-5%29%5E2+%2A%28x%2B5%29%5E2.

If you need more help with this important topic of factoring, then please see my website, by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take the third link on the homepage, which is "Basic Intermediate and College Algebra: One Step at a Time." Click on "Basic Algebra", and look for "Chapter 2", which has several sections on FACTORING. Many solutions to problems in these pages are then posted on the MATH IN LIVING COLOR pages, where they are solved in color.

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