How to simplify this square $(3 \times 4 + 2)^2$? If I have this $(3 \times 4 + 2)^2$,
How can I simplify it with out the final result.
Do I distribute the $^2$ over each number like this:
$(3^2 \times 4^2 + 2^2)$?
What is the rule?

No you can't distribute the powers like what you did.
There is a theorem called the binomial theorem that controls this type of operations.
The result is clearly $196$. Here is one way to get this result (steps are simplified so that you can follow)
You can do this to simplify the expression:
$$x=(3\cdot4+2)^2$$
then
$$x=(12+2)(12+2)$$
$$x=(12\cdot12)+2\cdot(12\cdot2)+(2\cdot2)$$
$$x=144+48+4 = 196$$
An expression like:
$$x=(a+b)^2$$
can be written as:
$$x=(a+b)(a+b)=a\cdot a+2\cdot a\cdot b+a\cdot a = a^2+2ab+b^2$$
