i know i have posted two thread at once but i am extremely in a hurry , i am sorry for this ,

OK. I would have thought that was harder than (e).

Do you know what coefficient means?
 
OK You're used to using n for the power. In this case n = 7. Maybe I should have just said the general term

The general term, in this case, is \(\displaystyle ^7C_r (x)^r (-x^2)^{7-r}\). Agree?
 
Ok so simplify the expression after the coefficient. For the power of x to be 10 what is r? And therefore what is the coefficient?
 
Is it 35 or -35?

There are 2 ways to do these expansions if a subtraction is involved:

1. \(\displaystyle (a-b)^7 =a^7 - ^7C_1a^6 b^1 + ^7C_2a^5b^2 - ^7C_3a^4b^3 \)……..etc, where you alternate signs

OR

2. \(\displaystyle (a +(-b))^7 = a^7 + ^7C_1a^6 (-b)^1 + ^7C_2a^5(-b)^2 +^7C_3a^49(-b)^3\)…....etc where everything is added and you keep the neg sign with the b and because of the odd powers of a neg number the signs will alternate (the first method is easier)

You have mixed the two, so that when your expression is simplified everything will be positive which is incorrect. Do one or the other but not both.
 
Harry_the_cat said:
Is it 35 or -35?

There are 2 ways to do these expansions if a subtraction is involved:

1. \(\displaystyle (a-b)^7 =a^7 - ^7C_1a^6 b^1 + ^7C_2a^5b^2 - ^7C_3a^4b^3 \)……..etc, where you alternate signs

OR

2. \(\displaystyle (a +(-b))^7 = a^7 + ^7C_1a^6 (-b)^1 + ^7C_2a^5(-b)^2 +^7C_3a^49(-b)^3\)…....etc where everything is added and you keep the neg sign with the b and because of the odd powers of a neg number the signs will alternate (the first method is easier)

You have mixed the two, so that when your expression is simplified everything will be positive which is incorrect. Do one or the other but not both.
Click to expand...
I got -35
 
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