SOLUTION: 1. 16a^4-2a 2. x^4-4x^2+3 Please Help, I am lost. Thanks

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: 1. 16a^4-2a 2. x^4-4x^2+3 Please Help, I am lost. Thanks      Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 55027: 1. 16a^4-2a


2. x^4-4x^2+3

Please Help, I am lost. Thanks
Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
I think you must need to factor these, you didn't give me the directions. If you neede something else let me know.
1. 16a%5E4-2a Factor out the GCF (greatest common factor).
2a%288a%5E3-1%29 Recognize that you have a difference of two cubes.
2a%282a%2A2a%2A2a-1%2A1%2A1%29
2a%28%282a%29%5E3-%281%29%5E3%29 The formula for factoring two cubes is highlight%28u%5E3-v%5E3=%28u-v%29%28u%5E2%2Buv%2Bv%5E2%29%29 u=2a and v=1
2a%282a-1%29%28%282a%29%5E2%2B2a%281%29%2B%281%29%5E2%29
2a%282a-1%29%284a%5E2%2B2a%2B1%29
:
2. x%5E4-4x%5E2%2B3
%28x%5E2%29%5E2-4%28x%5E2%29%2B3
Let p=x%5E2
p%5E2-4p%2B3 Factor as usual, two numbers that multiply to give you +3, but add together to give you -4 are:-1 and -3. (-3*-1=+3 and -1-3=-4)
%28p-3%29%28p-1%29
Let x%5E2=p
%28x%5E2-3%29%28x%5E2-1%29 Notice x%5E2-1 is the difference of squares, thushighlight%28u%5E2-v%5E2=%28u%2Bv%29%28u-v%29%29 applies.
%28x%5E2-3%29%28x%2B1%29%28x-1%29
Happy Calculating!!!