If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
0
Given m + n = 24, substitute n = 24 - m into the expression:
(m - 16)3 + (16 - m)3
Using the identity a3 + b3 = (a + b)(a2 - ab + b2) and simplifying:
(m - 16) + (16 - m) = 0
Thus, the expression evaluates to 0. Therefore, the correct answer is 0.
Important Questions from Algebric Equations
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
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?
