MODERATE EXERCISES  Expanding Binomials
(1) Use the Binomial Theorem to expand the expression
( x^{2} + 3x + 5 )^{4} .
(2) Use the Binomial Theorem to find the following terms:

(i) the middle term in the expansion of ( x^{2}  ^{1}/_{x} )^{12}
(ii) the term containing x^{4} in the expansion of ( x + 2y )^{10}
(iii) the term that does NOT contain x in the expansion of ( 2x^{2} + ^{1}/_{x} )^{9}
(3) Simplify the given expressions: (in (ii), this means factor)
(i) (x1)^{5} + 5(x1)^{4} + 10(x1)^{3} + 10(x1)^{2} + 5(x1) + 1 (ii) x^{5} + 10x^{4} + 40x^{3} + 80x^{2} + 80x + 32