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?
 A: 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:
$$x=(a+b)(a+b)=a\cdot a+2\cdot a\cdot b+a\cdot a = a^2+2ab+b^2$$
A: $(3 \times 4 + 2)^2 = (12 + 2)^2 = 14^2 =196$  while $(3^2 \times 4^2 + 2^2) = 9 \times 16 +4 = 144+4 = 148$, so that does not work.
If you want a rule for squares of sums, try: $$(x+y)^2 = x^2 + 2 x y +y^2.$$
A: Always go basic by using the order of operations:


*

*Parentheses.

*Exponents.

*Multiplication and division.(left to right)

*Subtraction and addition.(no same order)


Using the PEMDAS rule, first simplify the parentheses, then simplify the exponent(s). We have,$$ 3 \times 4 + 2$$in the parentheses. Notice that again, PEMDAS is applied. Multiplication is done before addition. So, the simplification of the parentheses is as follows. $$\begin{align}3 \times 4 + 2 & =  \color{maroon}{3 \times 4} + 2 \\ & = 12 + 2 \\ & = 14  \end{align}$$Now, the exponent. We'd have everything simplified as shown below: $$\begin{align} (3 \times 4 + 2)^2 & = & 14^2 \\ & =  & 14 \times 14 \\ & = & 196 \end{align} $$
A: No, you can't distribute the power on any operator,
power is distributed on $\times$ and $\div$ not on $+$ and $-$
A: Can you simplify $$(3\times4 + 2)?$$
then$$(3\times4 + 2)^2$$
by definition $a^2 = a\times a$
let a=$(3\times4 + 2)$
$$ = (3\times4 + 2)\times(3\times4 + 2)$$
multiplication before addition within the parentheses
$$ =(12 + 2) \times(12 + 2)$$
$$ =(14)\times(14)$$ 
$$= 196$$
The distributive property of multiplication applies to coefficients not to exponents.
a(b+c) = ab+ac
If the 2 was in front as a coefficient then you could write: 
$2(3\times 4 +2)$
$= 2\times3\times 4 +2\times 2$
The exponent sort of "distributes" when using the rule of exponents for a power of a product:
$$(ab)^m = a^mb^m$$
