You are Here: Home >< Maths

# Help with this sum watch

1. Ok so the question says

Hence, or otherwise show that

(y+1)^4 - y^4= (y+1)^3 + (y+1)^2 y + (y+1)y^2 + y^3

and deduce that

(y+1)^4 - y^4 < 4(y+1)^3

I don't know but for some reason when I calculate the first one I keep getting 5y^3 + 6y^2 + 4y. Does anyone know how to do this? I've been fighting this sum for an hour and it's really starting to bug me...
2. LHS-RHS
=(y+1)^4-(y+1)^3-(y+1)^2y-(y+1)y^2 - y^4-y^3
=(y+1)[(y+1)^3-(y+1)^2-(y+1)y-y^2 -y^3]
=(y+1)^2[(y+1)^2-(y+1)-y-y^2]
=(y+1)^3[(y+1)-1-y]
=0

second one take top equation away from bottom

0 < 3(y+1)^3 - (y+1)^2y-(y+1)y^2-y^3

I suppose you could expand the RHS and complete the square on it to show it is always >0
3. (Original post by noobynoo)
LHS-RHS
=(y+1)^4-(y+1)^3-(y+1)^2y-(y+1)y^2 - y^4-y^3
=(y+1)[(y+1)^3-(y+1)^2-(y+1)y-y^2 -y^3]
=(y+1)^2[(y+1)^2-(y+1)-y-y^2]
=(y+1)^3[(y+1)-1-y]
=0

second one take top equation away from bottom

0 < 3(y+1)^3 - (y+1)^2y-(y+1)y^2-y^3

I suppose you could expand the RHS and complete the square on it to show it is always >0
Thanks alot!
4. (Original post by LStudent)
Thanks alot!
If you find out the real answer post it I'd be interested to see what the the proper way of doing it was!
5. (Original post by noobynoo)
If you find out the real answer post it I'd be interested to see what the the proper way of doing it was!
It doesn't give an answer...here's the report from CxC:
"The substitution of x= y+ 1 was poorly done by many of the candidates."

Doesn't exactly tell one how to do the sum...

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 3, 2011
The home of Results and Clearing

### 3,215

people online now

### 1,567,000

students helped last year
Today on TSR

Hang on, have Edexcel's come out already?

### University open days

1. SAE Institute
Animation, Audio, Film, Games, Music, Business, Web Further education
Thu, 16 Aug '18
2. Bournemouth University
Fri, 17 Aug '18
3. University of Bolton
Fri, 17 Aug '18
Poll
Useful resources

Can you help? Study help unanswered threadsStudy Help rules and posting guidelinesLaTex guide for writing equations on TSR

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE