Answer: The required factored form of the given expression is [tex](4j+3)(4j+3).[/tex]
Step-by-step explanation: We are given to factor the following quadratic expression :
[tex]E=16j^2+24j+9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following factorization formula :
[tex]a^2+2ab+b^2=(a+b)^2=(a+b)(a+b).[/tex]
The factorization of expression (i) is as follows :
[tex]E\\\\=16j^2+24j+9\\\\=(4j)^2+2\times4j\times3+3^2\\\\=(4j+3)^2\\\\=(4j+3)(4j+3).[/tex]
Thus, the required factored form of the given expression is [tex](4j+3)(4j+3).[/tex]
