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Advanced difference of two squares

I will upload my working and question now. My question is that is there an efficient way of doing this instead of expanding complex polynomials and factorising them? Can this come up in the AQA maths a level exam?
I hate apple my account doesn’t let me post pics so I am using the app version
Reply 2
The images the bottom question is the one I’m stuck on
Reply 3
Original post by Mad Man
The images the bottom question is the one I’m stuck on

Image hasnt loaded properly.
Reply 4
I can’t seem to upload the question and my working so I’ll type it

[(2x+y)(y-2x)]^2-(4x^2+y^2+2z^2)^2

I noticed it was dots and I expanded the first bracket twice and the second once.

Is there a quicker way of doing this and will it come up in the exam. I think this is very tedious

Ps can someone help me upload images on tar iOS because it asks me to use a link but when I had my android I could take a pic and show it
Reply 5
Original post by Mad Man
I can’t seem to upload the question and my working so I’ll type it

[(2x+y)(y-2x)]^2-(4x^2+y^2+2z^2)^2

I noticed it was dots and I expanded the first bracket twice and the second once.

Is there a quicker way of doing this and will it come up in the exam. I think this is very tedious

Ps can someone help me upload images on tar iOS because it asks me to use a link but when I had my android I could take a pic and show it

The first bracket gives
(y^2-4x^2)^2
Then its simply doing dots as usual so
(sum)(difference)
and you pretty much write down the answer. Should be two (at most three) simple lines.

Theres the "new tsr" thread for reporting problems with it.
(edited 3 months ago)
Reply 6
Original post by mqb2766
The first bracket gives
(y^2-4x^2)^2
Then its simply doing dots as usual so
(sum)(difference)
and you pretty much write down the answer. Should be two (at most three) simple lines.

Theres the "new tsr" thread for reporting problems with it.

I still don’t get it can you show me?
It’s not homework it’s from the cgp textbook
Reply 7
Original post by Mad Man
I still don’t get it can you show me?
It’s not homework it’s from the cgp textbook

Dots is
a^2 - b^2 = (a+b)(a-b)
so here a=(y^2-4x^2) and b=(4x^2+y^2+2z^2). So ...

Obv in a+b the 4x^2 term disappears and in the a-b, the y^2 term disappears.
Reply 8
Original post by mqb2766
Dots is
a^2 - b^2 = (a+b)(a-b)
so here a=(y^2-4x^2) and b=(4x^2+y^2+2z^2). So ...

Obv in a+b the 4x^2 term disappears and in the a-b, the y^2 term disappears.

Your explanation is so much better than the book it factorises and does unnecessary steps but I get it now. TY

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