Final bits

Question 1

x^3 - a^3 =

x^3 + a^3 =

Answer 1

(x-a)(x^2+ax+a^2)

x+a)(x^2-ax+a^2

Question 2

Order matters,
no repeats
repeats

Answer 2

Combination
n!(n-r)!
(r+n-1)!/r!(n-r)! –> 6 chocolates, 3 people, 2 divisors, 10 letter word, 8!/2!6!

Question 3

order does not matter, all elements used,

all elements different
all elements are not different

Answer 3

Permuatations
n! –> ABCDEF
n!/a!b!c!… –> AABBB, BANANA

Question 4

order does not matter, not all elements are used

repeated elements
no repeated elements

Answer 4

n^r (r positions n elements)

n!/(n-r)!

Question 5

finding the common difference twice to get quadratic for summation of a sequence/series

Answer 5

cos(ax) changes domain and solutions

Question 6

proof by induction: n=1, k, k+1 then conclusion

Answer 6

triangle = 0.5 * b * perpendicular height to the base