### Theory:

The numeric expression refers to any record of numbers, signs of arithmetic operations and brackets, made up with meaning.

**For example:**

$3+5\cdot \left(7-4\right)$ is an numeric expression.

$3+:-5$ is not a numerical expression.

An algebraic expression is a record of letters, signs of arithmetic operations, numbers and brackets, made up with meaning.

**For example:**${a}^{2}-3b$ is an algebraic expression.

Since the letters that make up the algebraic expression can be assigned different numerical values (i.e., the meanings of the letters can be changed), these letters are called variables.

Algebraic expressions can be very cumbersome, and algebra teaches to simplify them using rules, laws, properties, formulas.

When simplifying calculations, the laws of addition and multiplication are often used.

**Addition of algebraic expressions:**

- Whenever it comes to adding algebraic terms, we add the coefficient of like terms together. i.e. coefficient of the variable with its like variable co-efficient and constant with constant.

Example:

To add $9x,4x$ and $2x$ where \(x\) is a variable, we add the coefficients alone, that is,

$9x+4x+2x=(9+4+2)x=15x$.

$9x+4x+2x=(9+4+2)x=15x$.

- In the same way, algebraic expressions can be added.

Example:

Let us add $(9y+7);(5y-3)$

Hence,

$\begin{array}{l}(9y+7)+(5y-3)\\ =[9y+5y]+[7+(-3)]\\ =[(9+5)y]+[7-3]\\ =14y+4\end{array}$

**Addition laws**

1) The amount does not change from a change in the places of the terms, i.e.

$a+b=b+a$

$a+b=b+a$

This is the translational law of addition.

2) To add the third term to the sum of two terms, we can add the sum of the second and third terms to the first term, i.e.

$\left(a+b\right)+c=a+\left(b+c\right)$

This is the combined law of addition.

**Conclusion**:

If for specific values of the letters an algebraic expression has a numerical value, then the indicated values of the variables are called valid.

If for specific values of letter an algebraic expression does not make sense, then the indicated values of the variables are called invalid.

If for specific values of letter an algebraic expression does not make sense, then the indicated values of the variables are called invalid.

the value $a=-4$ is invalid, because with it there will be a division by zero, but you cannot divide by zero!