Question on Binomial Theorem

Deadly SG

Find the first three terms in the expansion of (1 + 2x)^6 in ascending powers of x. Hence, or otherwise, find the coefficient of x^2 in the expansion of [(1 + 2x)^6][(2 - x)^2].

Haven't really learnt Binomial Theorem yet but it's in my practice paper... thanks in advance Smile

CoolMyth SG

(1+2x)^6 = 1 + (6C1)(1)(6C5)(2x) + (6C2)(1)(6C4)(2x)^2 + ...

The () are all multiplication lah.

For the second part, just know (2-x)^2 = 4 - 4x + x^2 and then compute the product by brute force. Laughing

r0mE_27 SG

ans:

(1+2x)^6 = 1^6 + 6C1(1^5)(2x) + 6C2(1^4)(2x)^2 + ...

then later find the 2nd one

(2 - x)^2 = 2 + 2C1(2^2)(-x) + 2C2(2)(-x)^2

den x them. to see which will give u the power X^2

6C2(1^4)(2x)^2(2) + 6C1(1^5)(2x)6C1(1^5)(2x) + 1^6(2C2(2)(-x)^2) entire thing divide by x^2 = ANSWER

r0mE_27 SG

first part wrong liao la lol! (6C1)(1)(6C5)(2x) no need that one

CoolMyth SG

Originally posted by r0mE_27:

first part wrong liao la lol! (6C1)(1[b])(6C5)(2x) no need that one[/b]

Err...ok. Long time no use formula. Recalling it from memory. Laughing

<guest> SG

Brings me back to school days. I did binomial theorem expansion to few negative powers just to please my maths teacher to pass me Embarassed

Deadly SG

um sorry didn't really get it. can explain in simpler terms cuz I havent really been exposed to this topic yet.

r0mE_27 SG

the last part.

u needa get

1 times x^2 to get x^2
x times x to get x^2
x^2 times 1 to get x^2

hence u just cross multiply lo, those that get u x^2 and den just add them together

striderz_o405 SG

refer to the formulae sheet. Wink

wishboy SG

binomial theorem only got a few formula

for (1+x)^n,
T(r+1) = (nCr) * (x^r)

for (y-x)^n,
T(r+1) = (nCr) * [y^(n-r)] * (x^r)

using these 2 formula, u can find a specific term by substituting the number of the term into T which is r+1.
then r would be the number of the term minus 1
other values sub in oso to find that term

u oso can use them to find for x or y to the power of any number, uhh this one i dunno how to explain very well so i think nvm ba, let ur teacher teach u better

^tamago^ SG

ok first do u noe how to do a single binomal expansion?

Deadly SG

its okay la i managed to do the question with the help rendered in this thread already. thanks ppl Wink

eagle SG

Cool Cool Cool

r0mE_27 SG

you are welcome Very Happy

wishboy SG

my pleasure... Cool