We need to find the Least Common Multiple between 4x² - 9 and 4x² + 12x +9.
First, we need to factorize each expression:
4x² - 9 can be factorized using the difference of squares given by:
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Then:
[tex]4x²-9=(2x+3)(2x-3)[/tex]
Now, for 4x² + 12x +9
Can be factorized using:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Then:
[tex]4x²+12x+9=(2x+3)^2[/tex]
Now, we need to find the LCM between (2x+3)(2x-3) and (2x+3)².
Then, the LCM is (2x+3)²(2x-3).
The correct answer is the third option.
