Question

I need an answer to this with workings

pls type it if ur answering..cos file links aren't working
Expand (a-b)^7​

Answer 1

`a^7-7a^6b+21a^5b^2-35a^4b^3+35a^3b^4-21a^2b^5+7ab^6-b^7`

Explanation:

There are multiple ways of expanding a polynomial expression to a high degree. One way of doing it is to write out the problem in the multiplication form, multiply (a - b) by itself (7) times.

`(a-b)^7`

`=(a-b)(a-b)(a-b)(a-b)(a-b)(a-b)(a-b)`

Now simplify, multiply two terms together,

`=(a^2-2ab+b^2)(a^2-2ab+b^2)(a^2-2ab+b^2)(a-b)`

Repeat this process,

`=(a^4-4a^3b+6a^2b^2-4ab^3+b^4)(a^3-3a^2b+3ab^2-b^3)`

Repeat this process one final time,

`a^7-7a^6b+21a^5b^2-35a^4b^3+35a^3b^4-21a^2b^5+7ab^6-b^7`