What is the simplified value of the expression (785×785×785+215×215×215)/(785×785−785×215+215×215)?
Show answer & explanation
Correct answer: C
Explanation
Given:
(785³ + 215³) / (785² − 785×215 + 215²)
By the formula:
a³ + b³ = (a + b)(a² − ab + b²)
(785³ + 215³) / (785² − 785×215 + 215²)
= (785 + 215)(785² − 785×215 + 215²) / (785² − 785×215 + 215²)
= 785 + 215 = 1000