Question

Using the identity (a + b)2 = a2 + 2ab + b2, derive the formula for (a + b + c)2. Hence, find
the value of (2x - 3y + 4z)2.​

Answer 1

Step-by-step explanation:

hope it helps u all the best

Answer 2

Answer:

Step-by-step explanation:

We know :  ( a + b )2 = a2 + 2 a b + b2  , We find value of ( a + b + c )2 by using given identity , As :

⇒⇒[ ( a + b ) + c ]2    , Now we use given identity and get :

⇒⇒( a + b )2 + 2 ( a + b ) ( c )  + c2  

⇒⇒( a + b )2 + 2 a c + 2 b c + c2  

⇒⇒a2 + 2 a b + b2 + 2 c a+ 2 b c + c2  

⇒⇒a2 + b2 + c2 + 2 a b + 2 b c  + 2 c a

Hence,

( a + b + c )2  = a2 + b2 + c2 + 2 a b + 2 b c  + 2 c a

Now we use above formula to get value of ( 2 x - 3 y + 4 z )2  ,As :

⇒⇒[ 2 x + ( - 3 y ) + 4 z ]2  

⇒⇒ ( 2 x )2 + ( - 3 y )2 + ( 4 z )2 + 2 ( 2 x )( - 3 y ) + 2 ( - 3 y ) ( 4 z )  + 2 ( 4 z ) ( 2 x )

⇒⇒ 4 x 2 + 9 y 2 + 16 z 2  - 12  x y  - 24  y z + 16 z  x