SOLUTION: factor the polynomial 9a^6b^8c^6-4d^8

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor the polynomial 9a^6b^8c^6-4d^8      Log On


   

Question 146254: factor the polynomial

9a^6b^8c^6-4d^8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
9a%5E6b%5E8c%5E6-4d%5E8 Start with the given expression

%283a%5E3b%5E4c%5E3%29%5E2-4d%5E8 Rewrite 9a%5E6b%5E8c%5E6 as %283a%5E3b%5E4c%5E3%29%5E2

%283a%5E3b%5E4c%5E3%29%5E2-%282d%5E4%29%5E2 Rewrite 4d%5E8 as %282d%5E4%29%5E2


Now use the difference of squares. Remember, the difference of squares formula is A%5E2-B%5E2=%28A%2BB%29%28A-B%29 where in this case A=3 and B=2

9a%5E6b%5E8c%5E6-4d%5E8=%283a%5E3b%5E4c%5E3%2B2d%5E4%29%283a%5E3b%5E4c%5E3-2d%5E4%29 Plug in A=3a%5E3b%5E4c%5E3 and B=2d%5E4

So the expression

9a%5E6b%5E8c%5E6-4d%5E8

factors to

%283a%5E3b%5E4c%5E3%2B2d%5E4%29%283a%5E3b%5E4c%5E3-2d%5E4%29

Notice that if you foil the factored expression, you get the original expression. This verifies our answer.