how do i factorise this?:



p^2 + 2p + 1 - t^2
= (p+1)^2 - t^2
This is the difference of two squares, so it can be rewritten

To factorize the expression p^2 + 2p + 1 - t^2, we can follow these steps:

Step 1: Group the terms and look for any common factors in each group. In this case, we have p^2 + 2p + 1 as one group and -t^2 as another group.

Step 2: Notice that p^2 + 2p + 1 is a perfect square trinomial, which means it can be factored further. In this case, it is the square of (p+1): (p+1)^2.

Step 3: Rewrite the expression using the factored form. Replace p^2 + 2p + 1 with (p+1)^2:

(p+1)^2 - t^2

Step 4: Now we have a difference of squares, which can be factored using the formula: a^2 - b^2 = (a+b)(a-b).

Therefore, we can factorize the expression as:


So, the factorized form of p^2 + 2p + 1 - t^2 is (p+1+t)(p+1-t).