Which of the following is a factor of P36 – Q36?P9 – Q9P6 + Q6P4 – Q4All of the above

To find out which of the given options is a factor of P36 - Q36, we need to simplify the expression and check for common factors.

First, let's simplify P36 - Q36. Since both terms have the same exponent, we can use the difference of squares formula: (a^2 - b^2) = (a + b)(a - b).

Applying this formula, we have: P36 - Q36 = (P18 + Q18)(P18 - Q18)

Now, let's simplify the options one by one:

1. P9 - Q9: We can rewrite this as (P3)^3 - (Q3)^3, which is a difference of cubes. However, this does not match the simplified form of P36 - Q36, so P9 - Q9 is not a factor.

2. P6 + Q6: This does not match the simplified form of P36 - Q36, so P6 + Q6 is not a factor.

3. P4 - Q4: We can rewrite this as (P2)^2 - (Q2)^2, which is a difference of squares. This matches the simplified form of P36 - Q36, so P4 - Q4 is a factor.

Therefore, the correct answer is: P4 - Q4.