Because the "is" represents the equals sign, we must look at everything before "is" and set that equal to everything after. 

The first part of the sentence requires us to represent four times the sum of a number and one. This means we must find the sum of the number and one, then multiply this entire quantity by four. The sum of a number and one can be represented as 

If we were to then multiply  by four, we would write this as , because the entire quantity  must be multiplied. 

The second part of the sentence asks us to find four greater than the square of the difference between the number and six. This means we must first find the difference between the number and six, and then we must square this quantity. After we do that, we must increase that quantity by four.

The difference between a number and six is represented by

If we were to find the square of this quantity, we could write this as 

Because we want to write an expression that is four greater than this, we could write  

Thus, the final equation would be:

We begin with

We follow the order of P.E.M.D.A.S.

Parenthesis:

Exponents:

Multiplication:

No division needed, so addition:

Finally, subtraction:

To evaluate an expression use PEMDAS to dictate the order of operations. Thus we simplify the parentheses first:

 and 
next we move on to exponents so:

Next multiplication and division from left to right:

and finally we add:

To correctly solve this expression, you must follow the correct order of operations: Parentheses- ,

Exponents-,

Multplication/ Division-,

and Addition/Subtraction-.

To correctly solve this expression, you must follow the correct order of operations:

Parentheses (starting with parenthesis inside other parenthesis)- 

,

Exponents-

,

Multplication/ Division-

,

and Addition/Subtraction-

.

Use order of operations (PEMDAS) in order to simplify the expression:

PEMDAS means to do calculations in the following order.

P: Parentheses

E: Exponents

M: Multiplication

D: Division

Substituting in the above values we get our new equation to be:

.

A: Addition

S: Subtraction

From here we add and subtract from left to right

Order of operations is as follows: (P)arentheses, (E)xponenets, (M)ultiplication, (D)ivision, (A)ddition, (S)ubtraction, also known as PEMDAS.

In this particular scenario, we begin with the parentheses. . The equation is now .

From here, since there are no exponents, we proceed to the multiplication and division. , and . The equation is now , which yields the answer .

When we evaluate the function  at , we can first plug in  for  to get 

.

Since the power is even, we know that , since any negative number to an even power is always a positive number.

Since the function is , we first compute the exponent before mulitplying by .

So the final answer is 

Order of operations means we start with parentheses, then move on to exponents, then multiplication, then division, then addition and subtraction.

Thus, 

This is an order of operations, PEMDAS problem. PEMDAS stands for parentheses, exponents, multiplication, division, addition, and subtraction.

First we evaluate the parentheses.  .  

Then, we evaluate the exponent.   , since everything raised to the zeroth power equals .  

Then, we do the division.    

Lastly, we add the . 

Putting it all together, we have .