Question 1059840: Could you please help me with binomial theorem. Step by step. I don't understand it. (X to the 3rd power minus the radical of y) to the 8th power. Thank you!
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52781)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Could you please help me with binomial theorem. Step by step. I don't understand it. (X to the 3rd power minus the radical of y) to the 8th power. Thank you!
Is this the same as the one posted earlier? This one is a difference, while the other is a sum.
Anyway, I'll show you the previous one, and if it's different you should be able to follow the same concept.
There's a little easier way to do this.
 , or 
 <======= Compare to this, and you'll see that: a = x3, b =  , and n = 8
Since it's a binomial raised to the 8th power you can use the 9th row of PASCAL'S TRIANGLE to get the COMBINATION VALUES for each term.
That 9th row has the following COMBINATION VALUES: 1 8 28 56 70 56 28 8 1
1 + 8 + 28 + 56 + 70 + 56 + 28 + 8 + 1
 ------------ Entering values for a and b after each term's COMBINATION VALUE
 --- RAISing EACH "a" VALUE to the nth power, in descending order
 ------- RAISing EACH "b" VALUE, starting at the 0th power, up to the nth power
 ------- Changing 
Now, SIMPLIFY each term to get: 
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