looks like you are studying the binomial theorem
You MUST memorize some basic formulas
e.g.
for (a+b)^n
term(r+1) = C(n,r) (a^r)(b^(n-r))
so for (3x+9)^9
term6 = C(9,5)(3x)^5 y^4
= 126(243x^5)y^4
= 30618 x^5 y^4
b) what is the middle term for (3x + y^3)^8 ?
c) let that term be term(r+1)
= C(10,r) x^r (2y)^(10-r)
we are interested in the term containing x^7
so r = 7 and the term is
C(10,7) x^7 (2y)^3
= 120 x^7 8y^3
= 960 x^7 y^3
Find the specified term of the expansion in each of the following:
a.6th term of (3x + y)^9
b.Middle term of (3x+y^3)^8
c.The term in (x + 2y)^10 that involves x^7
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