how do i factorise this?:
p^2+2p+1-t^2
thx.
p^2 + 2p + 1 - t^2
= (p+1)^2 - t^2
This is the difference of two squares, so it can be rewritten
=(p+1+t)(p+1-t)
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:
(p+1+t)(p+1-t)
So, the factorized form of p^2 + 2p + 1 - t^2 is (p+1+t)(p+1-t).