Factorize:

a^2 -1 + 2b - b^2

a^2 -1 + 2b - b^2

= a^2 - (b^2 - 2b + 1)
= a^2 - (b-1)^2 , now we have a difference of squares
= (a + (b-1))(a - (b-1))
= (a+b-1)(a-b+1)

a2+1+b2-2b

a2+b2(-1+2)b

This is very useful for me.

Thanks ⭐️⭐️

ᴛʜɪꜱ ɪꜱ ᴠᴇʀy ᴜꜱᴇꜰᴜʟ ꜰᴏʀ ᴍᴇ.

ᴛʜᴀɴᴋᴜ⭐

To factorize the expression a^2 - 1 + 2b - b^2, we will break it down into simpler terms.

First, let's look at the expression a^2 - 1. This is a difference of squares because it can be written as (a - 1)(a + 1). The difference of squares formula states that a^2 - b^2 can be factored into (a - b)(a + b).

Now let's look at the expression 2b - b^2. This can be factored by taking out the common factor of b, resulting in b(2 - b).

Putting it all together, we have:

(a - 1)(a + 1) + b(2 - b)

So the factored form of the expression a^2 - 1 + 2b - b^2 is (a - 1)(a + 1) + b(2 - b).