Solve in factored form 9x^2 - 4
show steps.
To solve 9x^2 - 4 in factored form, we can use the difference of squares formula:
a^2 - b^2 = (a + b)(a - b)
In this case, a = 3x and b = 2. So, the factored form of 9x^2 - 4 is:
(3x + 2)(3x - 2)
To solve the quadratic equation 9x^2 - 4, let's first identify if it can be factored. The expression can be rewritten as the difference of squares:
9x^2 - 4 = (3x)^2 - 2^2
Applying the difference of squares formula:
a^2 - b^2 = (a + b)(a - b)
We can rewrite our expression as:
(3x + 2)(3x - 2)
Thus, the factored form of the quadratic equation 9x^2 - 4 is (3x + 2)(3x - 2).
To solve the expression 9x^2 - 4 and express it in factored form, follow the steps below:
Step 1: Observe that the given expression is a difference of squares, which follows the form a^2 - b^2. In this case, a^2 = (3x)^2 and b^2 = 2^2.
Step 2: Identify a as 3x and b as 2.
Step 3: Apply the formula for the difference of squares, which is (a - b)(a + b).
Step 4: Substitute the values of a and b into the formula, giving us (3x - 2)(3x + 2).
Therefore, the factored form of 9x^2 - 4 is (3x - 2)(3x + 2).