Before proceeding with the addition and subtraction of different algebraic expression, you should understand what like and unlike terms are. Consider the following algebraic expressions:
- 4x2 + 3x + 4y + 8x + 10x2
- 14x2 + 7x + 4y
In expression (a), we can see that there are two terms having the variables x2, they are 4x2 and 10x2. These are like terms. Similarly, in the same expression, 3x and 8x are also like terms. If you look at expression (b), none of the terms have the same variables. All the three terms in expression (b) are unlike terms.
It is important to know what like and unlike terms are because, while performing operations of addition and/or subtraction on different algebraic expressions, we cannot add or subtract unlike terms from each other. Let us understand this further by considering an example situation of baking a cake.
Addition of Algebraic Expressions
You decide to bake a cake, and you decide that you need 6 cups of flour where 1 cup costs 5 eggs cost and 4 packets of sugar which costs to make this cake.
Along with this, you need 2 packets of chocolate paste, where 1 packet costs . Combining all the requirements you get an algebraic expression and this represents the total cost of making the cake. After making your cake mix, you realise that the quantity of the ingredients used isn’t enough to make a cake of the required size.
Now you need 5 more cups of flour and 3 more packets of chocolate paste and the total cost of this addition is and now to calculate the total amount spent we have to add and . You can write it as given below. This is how two algebraic expressions are added.
+ 5f +3c
Subtraction of Algebraic Expressions
Something goes horribly wrong! You put the cake in the oven but it comes out burnt. Now you have a big burnt cake. Now, you have to bake this cake once more and with proper quantities of all the ingredients so that it doesn’t get spoiled again.
From what we know the cake was really huge so let’s reduce the cups of flour by 2 cups and the packets of sugar by 2 packets so now the total cost of all our ingredients will be subtracting 2f + 2s from 11f +5e +4s +5c so we represent it as
11f+5e +4s +5c
– 2f – 2s
9f +5e +2s +5c
So, now finally our cake which turned out to be perfect, costs 9f+5e+2s+5c.
Example of Addition and Subtraction of Algebraic Expressions
Consider an example.
3xy + 4xyz + 9y² + 8x +55xy +xyz -2x
How do we solve this?
The first step is arranging the like terms one below the other so that they can be easily identified.
Now, make sure to put correct signs before each of the terms otherwise your calculation may go wrong.Thereafter, Simple addition and/or subtraction of the coefficients of the like terms takes place.
In this case, we add 3xy and 55xy and 4xyz and xyz and subtract 8x and 2x while 9y² remains as it is since it is an unlike term as compared to other terms
Now the answers we obtain are 58xy and 5xyz and 6x and 9y²as it is.
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