A number is expressed as N=(x^2-169)+(x-13)^2

1. Factorise (x^2-169)+(x-13)^2 completely
2. Explain why N is an even number for any value of x
3. Hence, given that N=(83^2-169)+70^2, without evaluating for N, find the 2 factors of N which are between 10 and 100

Question

A number is expressed as N=(x^2-169)+(x-13)^2 

1. Factorise (x^2-169)+(x-13)^2 completely
2. Explain why N is an even number for any value of x
3. Hence, given that N=(83^2-169)+70^2, without evaluating for N, find the 2 factors of N which are between 10 and 100

myininaya · Answer

So have you expanded N first by doing (x-13)(x-13)?

myininaya · Answer

And then you will collect like terms for N and then you can factor it

myininaya · Answer

completely!

anonymous · Answer

2x(x-13) right? But for me the real problem is with the second and last number

myininaya · Answer

Where did the extra x come from?

myininaya · Answer

wait sorry

myininaya · Answer

There is something missing though

myininaya · Answer

$$x^2-169+(x-13)^2$$
$$x^2-169+(x^2-2(13)x+169)$$
Is this what you did?

myininaya · Answer

Gosh you are right Its late here

myininaya · Answer

Ok So you have 2x(x-13)
And it has the factors 2, x, x-13
Since it has the factor 2 , then that means N is divisble by 2 which means that N is ____?

anonymous · Answer

Eveeen ohohhhhh, of course, dang can't believe I missed that

anonymous · Answer

first two parts have been explained by @myininaya 
for the last part put x=83 in 2x(x+13)
u get 2*83*96..this means two factors are 83 and 96

anonymous · Answer

sorry the eq is 2x(x-13)..factors are 83 and 70

anonymous · Answer

Well, thanks to you guys, sorry I only got one medal to give