Let cost of Emma's phone = x
Given that cost of Sophie's phone = 640
Then ratio of their phones cost will be x:640 or x/640
Given that ratio of their phones cost is 7:8 or 7/8
So both ratios will be equal.


x=560
So the new ratio of the cost of their phones will be 560:640
Now we have to find about how much should the prices of their phones decrease in order to have a ratio of 9:11.
So let that decreased amount is k then we will get equation :

11(560-k)=9(640-k)
6160-11k=5760-9k
6160-5760=11k-9k
400=2k
200=k
Hence final answer is prices of their phones should decrease by 200 in order to have a ratio of 9:11.
This problem is a difference of squares. So to solve this you want to factor it out so you get two numbers that multiple to -9 and add to 0. That would be -3 and 3
f(x)=(x-3)(x+3)
So your solution when you set f(x) to 0 would be -3 and 3.
The property shown there is the distributive property.
It states that a(b + c) = ab + ac
Or a(b - c) = ab - ac
360 - because a right angle is 90° and there are 4 right angles in a circle , 90 x 4 = 360