Addition and Subtraction of Algebraic Expressions

In this video we shall learn about Addition and Subtraction of Algebraic Expressions.

Unlike and Like Terms

Like terms: Terms in which the literal coefficients are same are called like terms. For example, 8xy and 3xy are like terms

Unlike terms: Terms with different literal coefficients are called unlike terms. 8xy and 3y2 are unlike terms since their literal coefficients are not same.

Addition and subtraction in algebraic expressions is possible only with like terms. We cannot add 3 books and 4 pencils together because they are two unlike things but we can definitely add 3 books and 4 books since they are like things. Similarly, we can add or subtract 8xy and 3xy since they have same literal coefficients.

There can be various forms of addition and subtraction of algebraic expressions.

1) Monomial with monomial

8xy + 3xy = 11xy

2) Monomial with Binomial

8xy + (7y2 – 6xy) = 7y2 + 2xy

3) Trinomial with monomial

(x3 + 9xyz2 − xy + 6) + 8xy = x3+ 9xyz2 – 7xy + 6.

4) Polynomial with monomial

(x2 − 5x + 9) + 8xy = x2 − 5x + 8xy + 9 and so on.

Let us understand this better through more examples.

The following is a polynomial with six terms. To solve it we need to segregate the like terms together and then add or subtract according to the signs.

Question 1: 8xy+2y2+2xy- y2+4y3+3y2

                  = (8xy+2xy)+ (2y2-y2+3y2) +4y3

                  = 10xy+4y2+4y3

The next question too is a polynomial of six terms.

Question 2: (8xy+2y2+3y) +(2y2+4y-5xy)

                  = 8xy-5xy+3y+4y+2y2+2y2

                  = 3xy+7y+4y2

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