Which of the following must be true for an expression to be a difference of two squares?
(a) All variables are raised to an even power,
(b) There are only two terms or
(c) Both terms have negative coefficients.
Squares are the numbers that are the result of any whole number when raised to the power of 2. They have many interesting properties and applications.
Answer: Options (a) all variables are raised to an even power, and (b) there are only two terms, which are true for an expression to be a difference of two squares.
Let's understand the solution in detail.
Let's take an example to understand the solution.
Example: Subtract the squares of 6 and 5.
Hence, 62 - 52 = 36 - 25 = 11
In the above example, we see that only one of the terms has a negative coefficient. Hence, option (c) both terms have negative coefficients, which is not true.
Also, there are only two terms; hence (b) there are only two terms, which is true.
Since 2 is even, hence option (a) all variables are raised to an even power, which is also true.