Algebraic Proof help

[Wiltinglillies]

I am supposed to be helping with this. I can do (c), but totally stumped by questions (a) and (b). If I simplify the left side of (a) I just get 24, and for (b) I get -10.
Help!!!!

Let n be 1.

LHS: (1+5)² -(1+1)² = 36-4=32
RHS: 8(1+3)= 8×4=32

Same process for b

Are you remembering to multiply out the second term inside brackets, si the minus applies to all of it?

I’m not sure showing that it works if n=1 constitutes proof

For a

(n+5)(n+5) - (n+1)(n+1) = 8n + 24

(n2 + 10n + 25) - (n2 + 2n + 1) = 8n + 24

8n + 24 = 8n + 24

Can you photo the whole question?
Lougle's example only shows that that works for n=1 - are you meant to prove it more completely for all values of x?

The other way to do it is:

(n+5)²=n²+10n+25 (a)
(n+1)²=n²+2n+1 (b)

a-b is 8n +24 which is the same as 8(n+3)

Slow at posting, I agree with Catherine, are you forgetting to (n+5)^2 is actually (n+5)(n+5)?

Or what 10broken said!

You don't need to find a value for n. Just expand the brackets on both sides. So for a) you get:
LHS
n2+10n+25-(n2+2n+1)
Which is
n2+10n+25-n2-2n-1
Which simplifies to
8n+24

RHS
8n+8×3
is
8n+24

So the LHS is identical to the RHS

Multiply out the brackets on the left hand side

Collect together like terms

Factorise to make it look like the right

are you forgetting to (n+5)^2 is actually (n+5)(n+5)?
YES
Thank you!!!