Algebra - FOIL Bi/Tri nomials to the nth power

[Miike012]

I added an attachment with my question highlited.

How was the coeficient 6, 4, and 1 determined.

by rule 6 the coeficient should be 8*3/(2+1) = 8.

Please help.
Thank you.

 

[Bohrok]

It looks like you're supposed to look at the numbers in the line for Coefficients rather than the coefficients of the terms in the bottom line for Multiplying. The instructions on that page work out only if both terms in the binomial have a coefficient of 1.

 

[Miike012]

Ok well how am I suppose to figure out the coefficient if that line isn't given?

 

[Bohrok]

Instead of looking at the 8 in the bottom line, use the 4 right above it. Do the same thing for each following coefficient.

 

[Miike012]

did that already.. it turns out that if I used the 4 instead of the 8.. the next coef. would be 4 rather than 6.. which doesn't work.

 

[Bohrok]

Not only is that 2 in front of the b messing up the instructions, but that ² exponent is too...
Before you actually use the exponent on your b to get the next coefficient, divide it's exponent by the exponent that b has in the original binomial in parentheses; in this case divide the exponents of b by 2 before you actually use them to find the coefficient.

 

[Miike012]

thank you. it makes sense now. I will be starting calc this upcoming semester, will this technique be useful?

 

[Bohrok]

Probably not; I don't think I saw binomial expansions at all in calc I or II.