What is the factored form of these expressions?

1. d2 + 18d + 81

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

b. (d + 9) 2

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

d. (d - 9) 2

2. d2 + 22d + 121

a. (d + 11) 2

b. (d - 11) 2

c. (d - 11) (d + 11)

d. (d - 121) (d - 1)

3. r2 - 49

a. (r - 7) (r + 7)

b. (r + 7) (r + 7)

c. (r - 7) (r - 7)

d. (r - 7) (r + 9)

To factor out the expressions, we need to find two integers where the sum is equal to the coefficient of the second term and the product of the integers is equal to the constant.

1. d2 + 18d + 81

x1 = 9 : x2 = 9

9+9 = 18

9x9 = 81

(d + 9) 2

2. d2 + 22d + 121

x1 = 11 : x2 = 11

11+11 = 22

11x11 = 121

(d + 11) 2

3. r2 - 49

x1 = - 7 : x2 = 7

-7 + 7 = 0

-7x7 = - 49

(r - 7) (r + 7)