Princess poly showed that (9+2i)(3−5i)−(9+i)(3−5i) is equal to 15+9i as shown in the table with her justifications. statements - reasons 1 (9+2i)(3−5i)−(9+i)(3−5i) given 2 (3−5i)(9+2i−9+i) factor out (3−5i). 3 (3−5i)(9−9+2i+i) commutative property of addition 4 (3−5i)(3i) combine like terms. 5 3(3i)−5i(3i) distributive property 6 9i−15i2 simplify. 7 9i−15(−1) substitution (i2=−1). 8 9i+15 simplify. 9 15+9i commutative property of addition which statement is true regarding her proof?

given expression:   (9+2i)(3−5i)−(9+i)(3-5i)

note: i have changed given to (9+2i)(3−5i)−(9-i)(3-5i) because there is some error in above provided given statement.

if we solve (9+2i)(3−5i)−(9+i)(3-5i), we get result 5+3i but final resuply suppose to be 15+9i as given in number 9 statement. ( 9. 15+9i)

we can see that (3−5i) is the common parenthesis.

so, we can factor out (3−5i) .

on factoring, we get

(3-5i) (9+2i - (9-

now, see..

we have minus sign in front of (9-i) parenthesis.

so, we need to distribute minus sign first, we get

(3-5i) (9+2i - 9+i).

combining like terms in second parenthesis, we get

(3-5i) (3i).

now, we can distribute 3i over (3-5i), we get

3*3i -5i*3i = 9i -15i^2.

= -1.

therefore, = -15(-1) = +15.

.

therefore, we can set it as:

given : (9+2i)(3−5i)−(9-i)(3−5i)  

note: i have changed given to (9+2i)(3−5i)−(9-i)(3-5i) because there is some error in above provided given statement.

if we solve (9+2i)(3−5i)−(9+i)(3-5i), we get result 5+3i but final resuply suppose to be 15+9i as given in number 9 statement. ( 9. 15+9i)

factor out (3−5i) : (3−5i)(9−9+2i+i).

commutative property of addition   : (3−5i)(9−9+2i+i).   : just swaping the positions of numbers.

combine like terms: (3−5i)(3i).

distributive property : 3(3i)−5i(3i)

simplify : 9i−15i^2

substitution () : 9i+15

commutative property of addition : 15+9i .

it could be 1,3 and more others to create a cylinder.

step-by-step explanation: