Factorise the following expression: 𝑧2+4𝑧+4z 2 +4z+4

The expression you provided is z^2 + 4z + 4. To factorise this, we need to find two numbers that multiply to 4 (the last term) and add to 4 (the coefficient of the middle term).

The numbers that satisfy these conditions are 2 and 2, because 2*2 = 4 and 2+2 = 4.

So, we can write the expression as:

z^2 + 2z + 2z + 4

Now, we can factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together:

z(z + 2) + 2(z + 2)

Now, you can see that (z + 2) is a common factor:

(z + 2)(z + 2)

So, the factorised form of the expression z^2 + 4z + 4 is (z + 2)^2.