Now It's Problems with Binomial Theorem...

[MathBaby]

Sorry for flooding this forum with weird questions... But as I went through the chapters I found more and more tough questions (maybe it's just tough for me)...

1. Find the coefficient of x^-12 in the expansion of (x³ - 1/x)^24.

For this question I don't know how to get the x^-12...

2.
a) Expand (2√2 + √3)^4 in the form a + b√6, where a and b are integers.
b) Find the exact value of (2√2 + √3)^5. (Answer: 698√2 + 569√3)

For question 2, I managed to get the answer for a) which is 217 + 88√6. But then I can't seem to get the answer for b)

[zaza]

You can solve both your questions in cunning ways. But for you, I suggest you just go down the road of writing the whole binomial expansion out, because the best way to get used to this is to see the whole thing. Once you understand the binomial expansion, then you can think about cutting corners.

You do know what the binomial expansion is right?

So for both these questions, just write out the whole thing. It'll take some time, but you'll understand a bit more by the end of it. Once you've done that, the answers will be apparent.


zaza

[Glaysher]

2b) (217 + 88√6)(2√2 + √3)

= 434√2 + 176√6√2 + 217√3 + 88√6√3

= 434√2 + 176√3√2√2 + 217√3 + 88√2√3√3

= 434√2 + 352√3 + 217√3 + 264√2

And I'll leave you to do the last step

I'd go with zaza's advice for question 1.