factor the expression given below 9x^2-16
Try using the standard form:
a^2-b^2=(a+b)(a-b)
and noting that
9x^2-16 = (3x)^2 - 4^2
To factor the expression 9x^2-16, we can use a method called the difference of squares.
The difference of squares states that for any two perfect squares A^2 and B^2, the expression A^2 - B^2 can be factored as (A + B)(A - B).
In our case, A^2 is equal to (3x)^2 and B^2 is equal to (4)^2.
So, let's apply the difference of squares to our expression:
9x^2 - 16 = (3x)^2 - 4^2
Now, we can rewrite the expression as follows:
9x^2 - 16 = (3x + 4)(3x - 4)
Therefore, the factored form of 9x^2-16 is (3x+4)(3x-4).