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.
Originally posted by Nathpoop: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
Another question, (no idea how to do)
3. Find in decending powers of x, the first four terms in the expansion of (2x - 1/2)^9. Hence obtain the coefficient of x^7 in the expansion of (1 - x)(2x - 1/2)^9
Originally posted by Nathpoop:Another question, (no idea how to do)
3. Find in decending powers of x, the first four terms in the expansion of (2x - 1/2)^9. Hence obtain the coefficient of x^7 in the expansion of (1 - x)(2x - 1/2)^9
(2x - 1/2)^9
= (-1/2)^9 (1-4x)^9
= (-1/2)^9 [ (-4x)^9 + 9C1(-4x)^8 + 9C2(-4x)^7 + 9C3(-4x)^6 + ... ]
= 512x^9 - 1152x^8 + 1152x^7 - 672x^6 + ....
Coefficient of x^7 in expansion of (1 - x)(2x - 1/2)^9
= ( 1152 X 1 ) + ( -672 X -1 )
= 1152 + 672
= 1824