Addition and Subtraction of Algebraic Expressions
In earlier classes, we have already become familiar with what algebraic expressions (or simply expressions) are. Examples of expressions are:
In the earlier classes, we have also learnt how to add and subtract algebraic expressions. Let's revisit it.
Example 1
Add: 7xy + 5yz – 3zx, 4yz + 9zx – 4y , –3xz + 5x – 2xy.
When doing addition of algebraic expressions: group the like terms (having same variable) together and add them up together. For eg: above 5 yz in the first expression and 4 yz in the second expression need to be added. There is no yz term in the third expression.
Upon doing so, we get: 7xy + 5yz –3zx + 4yz + 9zx – 4y –2xy – 3zx + 5x = (7xy - 2xy) + (5yz + 4yz) + (-3zx + 9zx - 3xz) - 4y + 5x =
Thus, the sum of the expressions is 5xy + 9yz + 3zx + 5x – 4y.
Note how the terms, – 4y in the second expression and 5x in the third expression, are carried over as they are, since they have no like terms in the other expressions.
Example 2
Subtract
Similar to addition of algebraic expressions, for subtraction as well, we group the like terms (having same variable) together and subtract them individually. For eg: above 5 x 2 7 x 2
So, we write: 7 x 2 − 4 xy + 8 y 2 + 5 x − 3 y - ( 5 x 2 − 4 y 2 + 6 y − 3 ). After removing the bracket, the signs of the terms within it are reversed thus, we get: 7 x 2 − 4 xy + 8 y 2 + 5 x − 3 y − 5 x 2 + 4 y 2 − 6 y + 3
Grouping the like terms: 7 x 2 − 5 x 2 − 4 xy + 8 y 2 + 4 y 2 + 5 x − 3 y − 6 y + 3
Which gives us: x 2 y 2
Thus, the subtraction of the expressions is 2 x 2 y 2
Note that subtraction of a number is the same as addition of its additive inverse. Thus, subtracting –3 is the same as adding +3. Similarly, subtracting 6y is the same as adding – 6y; subtracting –