Answer
$1024z^{10}$
Work Step by Step
$(a+b)^n = a^n + n/1!* a^{n-1}*b^1 + n(n-1)/2!* a^{n-2}*b^2 + n(n-1)(n-2)/3!* a^{n-3}*b^3 + . . . + b^n$
The first term is $a^n$.
The second term is $n/1!*a^{n-1}b^1$.
For each successive term, the power for $a$ decreases by one. Also, the power for $b$ increases by one.
The 11th term is as follows:
$n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7)(n-8)(n-9)(n-10)/11!*a^{n-11}*b^n$
$n=10$
$n(n-1)(n-2)(n-3)(n-4)(n-5)(n-6)(n-7)(n-8)(n-9)/10!*a^{n-
10}*b^n$
$10(10-1)(10-2)(10-3)(10-4)(10-5)(10-6)(10-7)(10-8)(10-9)/10!*a^{10-10}*b^10$
$10*9*8*7*6*5*4*3*2*1/11!*a^{10-10}*b^10$
$a^{10-10}*b^{10}$
$a^0b^{10}$
$b^{10}$
$b=2z$
$(2z)^{10}$
$2^{10}*z^{10}$
$1024z^{10}$
