What is the fifth term of #(x + y)^8#?

1 Answer
Jan 31, 2016

Use the formula #t_(r + 1) = _nC_r(a)^(n - r)(b)^r# to determine the #rth# term of the expansion.

Explanation:

Since we're looking for the 5th term, r = 4. The value of n is the exponent. "a" is the base to the left and "b" the one to the right.

#t_5 =_8C_4(x)^(8 -4)(y) ^4#

Calculating #""_8C_4# using the combination formula:

#""_nC_r# = #(n!) / ((n - r)!r!)#

#""_8C_4# = #(8!)/((8 - 4)!4!)#

#""_8C_4# = #(8(7)(6)(5)(4)(3)(2)(1))/(((4)(3)(2)(1))(4)(3)(2)(1))#

After simplifying:

#""_8C_4# = #1680/24#

#""_8C_4# = 70

#t_5 = 70(x^4)(y^4)#

#t_5 = 70x^4y^4#

So, term 5 has a value of #70x^4y^4#

Practice exercises:

  1. Find the middle term of #(2x - 3y)^12#

  2. Which term in #(4x + y)^11# would be constant?