Question

What is the difference in the total number of factors and the number of prime factors in 60^3 - 32^3 - 28^3

Answer 1

\(60^{3}- 32^{3} - 28^{3} =3\times 32\times 28\times 60\)

Answer 2

options :
1) 116
2) 120
3) 126
4) 130

Answer 3

Start with :
\(60-32=28\)

cube both sides
\((60-32)^3 = 28^3\)

For left hand side, recall the identity \((a-b)^3 = a^3-b^3-3ab(a-b)\) :
\(60^3-32^3 -3\cdot 60\cdot 32(60-32) = 28^3\)
\(\implies 60^3-32^3-28^3 = 3\cdot 60\cdot 32\cdot 28=2^9\cdot 3^2\cdot 5\cdot 7\)

Answer 4

so thats the prime factorization

do you know how to find the number of factors of a number from prime factorization ?

Answer 5

Yes.

Answer 6

good, see if you can finish the rest

Answer 7

Thank you :)