Question 16717: Hi, I'm having some trouble with factoring. I have two problems I'm getting stumped on. X4 + y4. that's x to the fourth + y to the fourth and the problem says to factor completely.
The other one is x3 + 3X2 - 25x - 75. that is X cubed plus 3 x squared minus 25 x -75. any help with these would be appreciated. thanks.
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Usually you can't do much to factor the SUM of two squares, but this one is special. You can complete the square on the middle term between the x^4 and y^4, which creates a difference of two squares problem to factor:
This would look nicer if you rearrange it:
It's still pretty ugly, but at least it is factored! A slightly better problem is to factor  . It factors without the use of square roots.
The second problem is a simple factoring by grouping problem. Just group the first two and the last two together. From the first two, you can take out a common factor of x^2, and from the second two, you can take out a common factor of 25:
Now, notice that (x+3) is a common factor, so you take out the (x+3), and what is left is the  .
Of course, the  is a difference of two squares, so it factors again:
R^2 at SCC
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