Complete the following exercises by applying polynomial identities to complex numbers. factor x2 + 64. check your work. factor 16x2 + 49. check your work. find the product of (x + 9i)2. find the product of (x − 2i)2. find the product of (x + (3+5i))2.

(a)

(b)

(c)

(d)

(e)

Step-by-step explanation:

(a)

we are given

we can also write as

now, we can use factor formula

we get

(b)

we are given

we can also write as

now, we can use factor formula

we get

(c)

we can use formula

so, we can write as

we can simplify it

and we get

(d)

we can use formula

so, we can write as

we can simplify it

and we get

(e)

we can distribute

so, we can write as

now, we can simplify it

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation:

555.99.

step-by-step explanation:

hope this