Answer:
[tex]\boxed{\pink{\sf (x + 3) \ is\ the \ LCM . }}[/tex]
Step-by-step explanation:
Given two expressions ,
[tex] \qquad (1)\: x^2 - 9 \\\\ \qquad (2)\:3x^3 + 81 [/tex]
And , we need to find the LCM , that is lowest common factor . So , let's factorise them seperately .
Factorising x² - 9 :-
[tex]= x^2 - 9 \\\\= x^2 - 3^2 \\\\ \red{= (x+3)(x-3)} \qquad\bf [Using \ a^2-b^2 = (a+b)(a-b) ][/tex]
Factorising 3x³ + 81
[tex]= 3x^3 + 81\\\\= 3(x^3+27) \\\\= 3( x^3+27) \\\\ = 3(x^3+3^3) \\\\ \red{= 3 [ (x+3)(x^2+9-3x) ] } \qquad \bf{[ Using \ a^3+b^3=(a+b)(a^2+b^2-ab) ] } [/tex]
Hence we can see that (x+3) is common factor in both expressions.
Hence the LCM is ( x+3 ) .
