6. Addition and subtraction of algebraic expressions

Addition and subtraction of algebraic expressions

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

For example:
3 + 5⋅(7−4) 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: a²−3b is an algebraic expression.
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.

Addition laws

1) The amount does not change from a change in the places of the terms, i.e.
 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.
 (a+b)+c=a+(b+c)

1)  This is the combined law of addition.
variable coefficient with its similar variable coefficient and constant with constant except that the fact we will include the term additive inverse.

Example:
To subtract  (12a + 7) from  (30a − 2), we have to add the additive inverse of (12a+7) with (30a−2).
Additive inverse of (12a + 7) is −(12a + 7)=(−12a − 7) 
Therefore,
(30a−2)−(12a + 7)=(30a −2) + (−12a −7)=(30a −12a)+(−2 −7)=18a −9