In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

For **example**, 2(3 + 8) is a numeric **expression**. **Algebraic expressions** include at least one variable and at least one operation (addition, subtraction, multiplication, and division).

In an **algebraic expression**, **terms** are the elements separated by the plus or minus signs.

Things to know

ORDERS OPERATIONS

I ASSUME THAT YOU HAVE BEEN PRIOR LECTURED ON THE SUBJECTS KIND A PEREQUISITES FOR TO SOLVE MATHEMATICAL COMPUTATIONS

WHAT ARE ORDERS OF OPERATIONS?

In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression.

The following is an example of a mathematical computation and to be able to solve it one must follow a list of protocol or set of rules.

4x-(2-3x)-5

What exactly are the orders of operations?

First we check if we have Brackets [ ] and check for other orders or operations inside the brackets

Second we check if we have have Parentheses ( ) and follow the operation or orders of operations as we could have operations inside the parentheses or grouping

Third we look for any powers or superscripts 1² or 2² which is simply means numbers multiplied as many times as indicated or given powers in this case the number 2 was given a power of ² so we can multiply it by itself 2 times and if it would have been given a power of 3 or 2³ we would have multiplied it 3x3x3 three times by itself or same number

Fourth We must check to see if we can divide from left to right

Fifth we check if there is any multiplication from left to right

Sixth we check to see if we can add from left to right

Seventh we check to see what we can subtract from left to right

I WAS ALLOWED TO COPY THE FOLLOWING VIDEO SO I ASSUME IT IS LEGAL TO SHARE

I COPIED AND PASTED

https://youtu.be/dAgfnK528RA

**NOW THAT I HAVE YOUR ATTENTION**

An **operation**

a process in which a number, quantity, expression, etc., is altered or manipulated according to formal rules, such as those of addition, multiplication, and differentiation.

**PROBLEM**

4x-(2-3x)-5

**OPERATION?**

Is there any **BRACKETS**?

No

Is there **PARENTHESES**?

Yes

Let's start performing this operation by rewriting it

and I **BOLDED **or **DARKENED **what we will work on first but second operation rule because there was no first operation or brackets.

4x **-(2-3x)** -5

as you can see everything inside the parentheses and the negative or minus - sign is bolded or darkened.

We must perform first operation we must first distribute the negative sign inside both inside the parentheses truly we pretend to multiply by -1 ---- -1(2-3x)

which is -1+3x

**NOW THAT WE PERFORMED OR TAKEN FIRST STEPS IN OPERATING THE PROBLEM**

**ADDED NOTES**

**Here are the basic steps to follow to simplify an algebraic expression:**

- remove parentheses by multiplying factors.
- use exponent rules to remove parentheses in terms with exponents.
- combine like terms by adding coefficients.
- combine the constants

4x-(2-3x)-5

4x-2+3x-5 at this point you say question why didn't we change -5 to +5? because we

operated on everything inside parentheses **ONLY**

**4x **-2 + 3**x** -5 we followed basic steps added notes on simplifying algebraic expressions

4x and **Like terms** are mathematical **terms** that have the exact same variables and exponents but they can have different coefficients.

**7x **-2 -5

7x **-2-5 ** Now we combine **CONSTANTS**

7x-7

There is nothing else or no more operations

**7x-7 is an answer**

Some answers might reflect some **properties**

**DISTRIBUTIVE**

**7(x-1)**

Just like you distribute or use this property to remove parentheses you can also reinstate parentheses but you must ensure that both terms have a common

7x-7

There was a common number. The number 7 on both terms.

Coeffecient and constant

7 ( x - 1 )

If we use distributive property?

We multiply 7 to both inside parentheses we get 7x-7

We distributed the 7 to both variable and constant inside as parentheses means multiply when there is no sign in front or number in which prior we pretended to have a 1 so that we could use the rules for of multiplication of signs

Well I hope I helped

THE TEACH

Carmen S.

4x-(2-3x)-5 First you should distribute the minus. Note that -3x will become positive because the minus swaps the sign on the term. 4x-2+3x-5 Then combine like terms. 7x-7 Done.11/23/19