Answer: (A) [tex]2x^4+2x^3-12x^2[/tex] is the correct option.
Step-by-step explanation: We are given to expand the following expression :
[tex]E=2x^2(x+3)(x-2)~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To expand the given expression, we must multiply each term of every expression to each term of the other two expressions.
The expansion is as follows :
[tex]E\\\\=2x^2(x+3)(x-2)\\\\=2x^2(x^2+3x-2x-6)\\\\=2x^2(x^2+x-6)\\\\=2x^4+2x^3-12x^2.[/tex]
Thus, the required expended form is [tex]2x^4+2x^3-12x^2.[/tex]
Option (A) is CORRECT.
