How do i solve this two questions, confused over her.
1.
(x^2 + 1/x)^7, write down and simplify the forth term (Ans:
35x^5) (I cant seem to get the power right, i've only got the
coefficient of x right.)
2.
The coefficient of x^4 in the expansion (1 + kx)(1 - 2x)^8 is
-224. Find the value of k. (Ans: k = 3)
Regards, thanks.
1.
4th term of (x^2 + 1/x)^7
= 4th term of ( x^2 )^7 ( 1 + 1/x^3 )^7
= 4th term of (x^14) ( 1+ 1/x^3 )^7
= 7C4 X (x^14) X (1^4) X ( 1/X^3 )^3
= 35 X (x^14) X ( 1/X^9 )
= 35x^5
2.
Lets look at (1 - 2x)^8 first.
Term carrying x^3
= 8C5 X (-2x)^3
= -448x^3
Term carrying x^4
= 8C4 X (-2x)^4
= 1120x^4
Now looking back at (1 + kx)(1 - 2x)^8, you will realise the
coefficient of the term that carries x^4 will be
= (-448 X k) + (1120 X 1)
= -448k + 1120
And since the coefficient of x^4 is -224,
-224 = -448k + 1120
k = 3