Option C: [tex](4 j+3)^{2}[/tex] is the correct answer.
Explanation:
The given expression is [tex]16 j^{2}+24 j+9[/tex]
We need to factor the expression.
Let us rewrite the expression as
[tex](4j)^{2}+24 j+(3)^2[/tex]
Also, we can rewrite the term [tex]24j[/tex] as [tex]2(4)(3)j[/tex]
Thus, we have,
[tex](4j)^{2}+2(4j)(3)+(3)^2[/tex]
Hence, the equation is of the form,
[tex](a+b)^{2}=a^{2}+2 a b+b^{2}[/tex]
where [tex]a=4 j[/tex] and [tex]b=3[/tex]
Hence, the factor of the expression can be written as [tex](4 j+3)^{2}[/tex]
Thus, the factored expression is [tex](4 j+3)^{2}[/tex]
Therefore, Option C is the correct answer.
