14) Factor each of the following expressions
a) 9x2 – 3x
b) 4x2 – 9
a) 3x(3x-1)
b) (2x-3)(2x+3)
a) To factor the expression 9x^2 - 3x, we can look for a common factor among the terms. In this case, the common factor is 3x. We can factor out 3x from both terms, resulting in:
3x(3x - 1)
So, the factored form of 9x^2 - 3x is 3x(3x - 1).
b) To factor the expression 4x^2 - 9, we can observe that it is a difference of squares. The expression can be rewritten as (2x)^2 - 3^2.
Using the formula for the difference of squares, we can factor this expression as:
(2x + 3)(2x - 3)
So, the factored form of 4x^2 - 9 is (2x + 3)(2x - 3).