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In a difference of squares problem terms must be perfect squares?
coefficient
In a difference of squares problem both terms must be what squares?
Perfect
In a difference of squares binomial the exponents of the variables must be?
They must be even.
In a difference of squares problem both terms must be squares?
perfect * * * * * Not strictly. they could both be multiples of sqaures. For example, factorise 3x3 - 48x. Neither term is a square but they do become squares when the common factor, 3x, is separated out. Also, when rationalising surds, one would use the difference of two squares but (at least) one of the terms is not a square.
What do you notice about the difference between squares of consecutive numbers?
The difference between the squares of two consecutive numbers is the sum of those two numbers. For example: 2 squared is 4. 3 squared is 9. 9-4=5 2+3=5 This is for a very simple reason: To go from 2x2 or '2 lots of two' to '3 lots of two' (3x2) we must add another two. 3 lots of two equals 2 lots of three. To get to three lots of two we need another three. We have added two then three, or 2+3. You can also apply this rule two numbers further apart, but to discover their squares' difference you must add them together and multiply by their difference EG. 2 squared is 4 4 squared is 16 16-4= 12 (2+4)x2=12
