Quick check of 4 term polynomial factorised

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The discussion revolves around the factorization of the polynomial expression at^2 - 4a + 2t^2 - 8. The user initially groups the terms and attempts to factor them, leading to the expression (a+2)(t^2-4). A participant points out a typo in the user's factorization, clarifying that the first term should be a(t^2 - 4) instead of a(t^2 - 4a). The user correctly identifies that the term (t^2 - 4) can be factored further using the difference of squares, resulting in the final answer of (a+2)(t-2)(t+2). The overall consensus is that the user is on the right track, with minor corrections needed in their initial steps.
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Could someone quickly go over my working, as I am not 100% sure I have done it the right way. I will show and explain my working step by step.

$$ at^2-4a + 2t^2-8$$

I first grouped the values: (at^2-4a) + (2t^2-8)

I then factorised these equations into: a(t^2-4a) + 2(t^2-4)

I then regrouped: (a+2) (t^2-4)

This is the part I am not sure is right, I the thought to factor more I could change the 4 to 2^2 which would give (t^2-2^2) which gave me the difference of two squares; right?

I then got the final answer of: (a+2)(t-2)(t+2).

I would just like to know if this is the right way of doing a equation like this, if not could someone show where I have gone wrong.
 
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Looks good to me. You can always multiply out your final answer and see if it comes out to your original equation.
 
Taylor_1989 said:
Could someone quickly go over my working, as I am not 100% sure I have done it the right way. I will show and explain my working step by step.

$$ at^2-4a + 2t^2-8$$

I first grouped the values: (at^2-4a) + (2t^2-8)

I then factorised these equations into: a(t^2-4a) + 2(t^2-4)
You have an error (maybe a typo) above. The first term should be a(t2 - 4).
Taylor_1989 said:
I then regrouped: (a+2) (t^2-4)

This is the part I am not sure is right, I the thought to factor more I could change the 4 to 2^2 which would give (t^2-2^2) which gave me the difference of two squares; right?

I then got the final answer of: (a+2)(t-2)(t+2).

I would just like to know if this is the right way of doing a equation like this, if not could someone show where I have gone wrong.
 
Yeah it was a typo, my bad.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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