what are the factored forms of the following expressions?

d^2+18d+81

a) (d+9) (d-9)

b) (d+9)^2

c) (d-81) (d-1)

d) (d-9)^2

also if anyone knows the whole test thats helpful <3

since 9 = 18/2, that makes B the answer

To find the factored form of the expression d^2 + 18d + 81, we can use a method called "factoring by grouping."

Step 1: Notice that the coefficient of the middle term (18d) is twice the square root of the last term (81). This indicates that the expression might be a perfect square trinomial.

Step 2: Take the square root of the first and last terms: √d^2 = d, and √81 = 9.

Step 3: Split the middle term (18d) using the values from step 2: 9d + 9d.

Step 4: Factor by grouping:
d^2 + 9d + 9d + 81

Step 5: Factor out the common terms from the first two and the last two terms separately:
d(d + 9) + 9(d + 9)

Step 6: Notice that (d + 9) is common to both terms:
(d + 9)(d + 9)

So, the factored form of the expression d^2 + 18d + 81 is (d + 9)(d + 9), which is equivalent to (d + 9)^2.

Now, let's check the options provided:

a) (d + 9)(d - 9) - This is not the correct factorization.
b) (d + 9)^2 - This is the correct factorized form.
c) (d - 81)(d - 1) - This is not the correct factorization.
d) (d - 9)^2 - This is not the correct factorization.

So, the correct factorized form of the expression is (b) (d + 9)^2.