If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
1
We are given that m + n = 24. Using the identity for the sum of cubes:
(a - b)³ + (b - c)³ = (a - b + b - c)((a - b)² + (b - c)² + (a - b)(b - c))
Substitute m + n = 24, and apply the simplification. After solving, we get 1 as the result.
Thus, the correct answer is option 1: 1.
Important Questions from Algebric Equations
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)If a³ + b³ = 28 and a + b = 4, then what is the value of ab?
