Question

Which of the following is the expansion of (2m - n)7?

Answer 1

Explanation:

Given is an algebraic term 2m-n raised to power 7.

We can use binomial theorem to expand this.

Binomial theorem says that

`(x+a)^n = x^n+nax^(n-1) +...nCrx^(n-r) a^(r) +...+a^n`

Here we have I term as 2m and II term = -n

Hence applying the formula for n =7

we have

`(2m-n)^7 = (2m)^7+7(2m)^6(-n)+7C2(2m)^5(-n)^2+7C3(2m)^4(-n)^3+7c4(2m)^3(-n)^4+7C5(2m)^2(-n)^5+7C6(2m)^1(-n)^6+(-n)^7\\=128m^7-448m^6n+672m^5n^2-560m^4n^3+280m^3n^4-84m^2n^5+14mn^6-n^7`

Answer 2

(2m - n)⁷ can be expanded using the binomial theorem or pascal's triangle, but writing out the work is proving to be really difficult. the application of the theorem is pretty complicated and it isn't easy to format in this textbox.

the expansion of this would be 128m⁷ - 448m⁶n + 672m⁵n² - 560m⁴n³ + 280m³n⁴ - 84m²n⁵ + 14mn⁶ - n⁷. let me know if you're genuinely lost on how to find it and i'll give a written explanation a shot, but i'd really, really encourage you to refer back to your notes if you took any in class (or the lesson, if it's an online class) and see if you can find anything which explains the binomial theorem or pascal's triangle. both of those will help you immensely.