Solve the following
(a + b + c) (ab + bc + ca) - abc = ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. (a + b) (b + c) (c + a)
| Understanding | Application |
| Tricks |
(a + b + c) (ab + bc + ca) - abc = (a2b + abc + a2c +b2a + b2c + abc + abc + bc2 + ac2) - abc = (a2b + 2abc + a2c +b2a + b2c + bc2 + ac2) ........i) |
| Now |
From option (a + b) (b + c) (c + a) ⇒ (ab + ac + b2 + bc)(c + a) ⇒ (abc + a2b +ac2 + a2c + b2c + b2a +bc2 + abc) ⇒ (2abc + a2b +ac2 + a2c + b2c + b2a +bc2) .........ii) |
| Hence |
From eq i) and eq ii) both are same So (a + b) (b + c) (c + a) |