factorise:
d2 + 2d + 1 - e2
(d+1)^2 - e^2
Since that is the difference of two squares, it can also be written
(d + 1 + e)(d +1 -e)
or (d + e + 1)(d -e +1)
To factorize the given expression d^2 + 2d + 1 - e^2, we can rewrite it as a difference of squares by treating the first three terms as a perfect square.
The expression d^2 + 2d + 1 can be factored as (d + 1)^2, using the identity (a + b)^2 = a^2 + 2ab + b^2.
The expression -e^2 can be factored as -(e)^2, which can be further simplified as -e^2.
Combining these factors, we have:
d^2 + 2d + 1 - e^2 = (d + 1)^2 - e^2
Now, we have a difference of squares. This can be factored as follows:
(d + 1)^2 - e^2 = (d + 1 - e)(d + 1 + e)
Therefore, the factorized form of the expression d^2 + 2d + 1 - e^2 is (d + 1 - e)(d + 1 + e).