CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Prove that (x+y)4=x4+4x3y+6x2y2+4xy3+y4.

Open in App
Solution

(x+y)4=x4+4x3y+6x2y2+4xy3+y4
First take L.H.S (x+y)4
So, the above expression is written as ((x+y)2)2
We know that (x+y)2=x2+2xy+y2,(x+y+z)2=x2+y2+z2+2xy+2yz+2zx
Therefore, (x2+2xy+y2)2
Here, x=x2,y=2xy,z=y2
So, (x2+2xy+y2)2=x4+4x2y2+y4+4x3y+4xy3+2y2x2
= x4+4x3y+6x2y2+4xy3+y4
L.H.S = R.H.S
x4+4x3y+6x2y2+4xy3+y4=x4+4x3y+6x2y2+4xy3+y4
Hence (x+y)4=x4+4x3y+6x2y2+4xy3+y4 is proved.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Puzzles with Digits
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon