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

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Answer 1 · 2016-01-31T18:09:16

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

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:

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