1
Q
x^3 - a^3 =
x^3 + a^3 =
A
(x-a)(x^2+ax+a^2)
x+a)(x^2-ax+a^2
2
Q
Order matters,
no repeats
repeats
A
Combination
n!(n-r)!
(r+n-1)!/r!(n-r)! –> 6 chocolates, 3 people, 2 divisors, 10 letter word, 8!/2!6!
3
Q
order does not matter, all elements used,
all elements different
all elements are not different
A
Permuatations
n! –> ABCDEF
n!/a!b!c!… –> AABBB, BANANA
4
Q
order does not matter, not all elements are used
repeated elements
no repeated elements
A
n^r (r positions n elements)
n!/(n-r)!
5
Q
finding the common difference twice to get quadratic for summation of a sequence/series
A
cos(ax) changes domain and solutions
6
Q
proof by induction: n=1, k, k+1 then conclusion
A
triangle = 0.5 * b * perpendicular height to the base
