If a + b = 2c, then which of the following identities is always true?
2024
If a + b = 2c, then which of the following identities is always true?
- A.
a² + 2ac = b² + 2bc
- B.
a² - 2bc = b² - 2ac
- C.
a² + 2bc = b² + 2ac
- D.
a² - ac = b² - bc
Attempted by 10 students.
Show answer & explanation
Correct answer: C
Correct answer: a² + 2bc = b² + 2ac
Start from the option to be tested:
a² + 2bc = b² + 2ac
Move like terms together:
a² - b² = 2ac - 2bc
Factor both sides:
(a - b)(a + b) = 2c(a - b)
Now use the given condition: a + b = 2c.
(a - b)(2c) = 2c(a - b)
Both sides are the same, so the identity is true for all values satisfying a + b = 2c.