Algebraic Simplification Test 3

Find the value of (x³+y³+z³ - 3xyz), if x +y+z = 9 and xy + yz+zx = 26:

 9 (x+y)² - 4x² can be factorised as:

If (x+2) and (x-1) are the factors of the polynomial x³ + 10x² + mx + n, then:

If a = 713 and b + c = 1429 and a³ + b³ + c³ – 3abc = 6426, then what will be the value of c ? , given a,b,c are consecutive no.

 The expression 5^2x - 2^3x has a factor-

 If x + y = 7, then what will be the value of x³ + y³ + 21xy? 

If x, y and z are real numbers such that (x – 3)² + (y – 4)² + (z – 5)² = 0, then (x + y + z) = ?

 4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ + 4⁶⁵ is divisible by: