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The square root of (3a + 2b + 3c)^(2) - ...

The square root of `(3a + 2b + 3c)^(2) - (2a + 3b + 2c)^(2) + 5b^(2)` is

A

`sqrt5 (a + b + c)`

B

`sqrt5 (a + b)`

C

`sqrt5 (a + c)`

D

`sqrt5 (a + c -b)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(3a + 2b + 3c)^(2) - (2a + 3b + 2c)^(2) + 5b^(2)`
`= (3a + 2b + 3c + 2a + 3b + 2c) (3a + 2b + 3c - 2a - 3b - 2c) + 5b^(2)`
`= (5a + 5b + 5c) (a -b + c) + 5b^(2)`
`= 5(a +c + b) (a +c -b) + 5b^(2)`
`= 5[(a + c^(2)) -b^(2)] + 5b^(2)`
`= 5 (a + c )^(2)`
`:.` Square root of the given expression is
`sqrt(5(a +c)^(2)) = sqrt5 (a +c)`
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