SOLUTION: Factor: 16x^4 – 2xy^3 It has been a while since I had Algebra, Trig, etc. 1. How do you express (say) this sequence above? 2. What is the answer? 3. Finally, please

Algebra ->  Exponents -> SOLUTION: Factor: 16x^4 – 2xy^3 It has been a while since I had Algebra, Trig, etc. 1. How do you express (say) this sequence above? 2. What is the answer? 3. Finally, please      Log On


   

Question 87669: Factor: 16x^4 – 2xy^3
It has been a while since I had Algebra, Trig, etc.
1. How do you express (say) this sequence above?
2. What is the answer?
3. Finally, please direct me to the appropriate page on your web site where I might be able to learn a little more about this, and perhaps "brush up" on what I have forgot?
Many, many thanks for your assistance,
Sam Genovese
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
16x%5E4+%96+2xy%5E3+

The first step is to factor out the common factor:
2x%288x%5E3+-+y%5E3%29+

Now, this is the difference of two cubes. There is a formula that goes like this:
x%5E3-y%5E3+=+%28x-y%29%28x%5E2+%2B+xy%2B+y%5E2%29+
Notice that this factors into a binomial times a trinomial. The binomial is pretty simple, but the trinomial is a bit harder. If you have never seen this before, you should see my website, which I will mention later.

Use this formula to factor as follows:
2x%288x%5E3+-+y%5E3%29+
2x%28%282x%29%5E3+-+y%5E3%29+
2x%282x-y%29+%28_____%2B____%2B_____%29+
2x%282x-y%29+%284x%5E2%2B2xy%2By%5E2%29+

See my website by clicking on my tutor name "rapaljer" anywhere in algebra.com, then look for MATH IN LIVING COLOR, go to Intermediate Algebra, and look for Section 2.01 Factoring the Sum and Difference of Cubes.

R^2 Retired from SCC