Final answer:
The expressions (2x - 3)(2x - 9), (2x + 3)(2x - 9), (2x - 3)(2x + 9), and (2x + 3)(2x + 9) are already in factored form and cannot be simplified further.
Step-by-step explanation:
To factor the polynomial, we examine each expression inside the parentheses and remember that if we are raising the entire expression to a power, this power affects everything inside the parentheses.
Let's look at each case:
- a) (2x - 3)(2x - 9): This is already factored, and there is no common factor or special product (like a difference of squares) that will simplify this further.
- b) (2x + 3)(2x - 9): As with part a), this expression is already in factored form and cannot be simplified further.
- c) (2x - 3)(2x + 9): This is factored and there are no further factors common between the two terms.
- d) (2x + 3)(2x + 9): This is also already factored and has no common factors or recognizable patterns for further simplification.
In each case, the expressions given are the final factored forms of the polynomials as there are no common factors or special products present in the terms.