Answer
12$x^{2}$$y$ - 27$y$ - 4$x^{2}$ + 9
= (12$x^{2}$$y$ - 27$y$) - (4$x^{2}$ - 9)
= 3$y$(4$x^{2}$ - 9) - (4$x^{2}$ - 9)
= (4$x^{2}$ - 9)(3$y$ - 1)
= (2$x$ + 3)(2$x$ - 3)(3$y$ - 1)
Work Step by Step
This polynomial must be factored. First, we start by grouping the four terms into groups of two, as seen in step 2. We factor out the 3y in the first group in step 3. Next, we combine the terms into two pairs as shown in step 4. In step 5, we can simplify the first group by factoring (4x^2 - 9) into (2x + 3)(2x - 3) by using the formula A^2 - B^2 = (A+B)(A-B). Thus, the final answer is (2x + 3)(2x - 3)(3y - 1)
