AS Maths C2 Binomial Expansion

Hey guys,
Is this the right place for this? I'm not to sure if its not just move it :smile:

Any way, can anyone explain to me how Binomial expansion works or point me towards somewhere I can find out. I have the Heinemann text book but I'm confused.

I get how you get the numbers from the triangle but how do you know which terms to multiply by what and which way round the powers go?

For Example:

(x+2y)^3

I understand that you look on the third row of the triangle or use the nCr button on the calculator to get the values but then how do you use them?

From the text book:

The coefficients are 1,3,3,1 which I understand and then its:

x^3 + 6x^2y + 12xy^2 + 8y^3

and I don't understand how you get that? Could anyone help me?

Thanks

Reply 1

Salinger

1

AKalair

Hey guys,
Is this the right place for this? I'm not to sure if its not just move it :smile:

Any way, can anyone explain to me how Binomial expansion works or point me towards somewhere I can find out. I have the Heinemann text book but I'm confused.

I get how you get the numbers from the triangle but how do you know which terms to multiply by what and which way round the powers go?

For Example:

(x+2y)^3

I understand that you look on the third row of the triangle or use the nCr button on the calculator to get the values but then how do you use them?

From the text book:

The coefficients are 1,3,3,1 which I understand and then its:

x^3 + 6x^2y + 12xy^2 + 8y^3

and I don't understand how you get that? Could anyone help me?

Thanks

using pascals triangle or NcR, the coefficients come out as 1 3 3 1

1 [(x)^3 (2y)^0] + 3 [(x)^2 (2y)^1] + 3 [(x)^1 (2y)^2] + 1 [(x)^0 (2y)^3

= 1x^3 + 3[x^2 * 2y] + 3 [x * 2y^2] + (2y)^3

= x^3 + 3[2x^2y] + 3[x*4y^2] + 8y^3

= x^3 + 6x^2 y + 12xy^2 + 8y^3

notice the powers in each part, always add up to 3. thats the key to remember