prove that a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−ab−bc−ca) . How can I solve this without expanding everything?

The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, find the numbers.

A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines started at 9 a.m while machine P closed at 11 a.m. and the remaining two machines complete the work. Approximately at what time will the work be finished?A. 11:30 a.mB. 12 noonC. 12:30 p.mD. 1 p.m

What number should be added to (7)/(12) to get (4)/(15) ?

2 men each working 5 hour per day can finish a job in 12 days. How long will 4 men each working 2 hours per day take to finish the same job?

State true or false. (i) Cube of any odd number is even. (ii) A perfect cube does not end with two zeros. (iii) If square of a number ends with 5, then its cube ends with 25. (iv) There is no perfect cube which ends with 8. (v)