"What are like terms and unlike terms?" , this question is having had by almost all the students who study 5th grade or below 5th grade in school.

**Like terms or Similar terms: **

**Like terms are the terms which have the same variables with same exponent for each variable.**

**Examples : 7x, 3x, - 4x**

**Unlike terms or Dissimilar terms: **

**Unlike terms are the terms which have same variables or different variables. **

**If they have same variables, the exponents will not be same. **

**Examples : 9x², 5xy, - 4xy², y, 6**

More clearly,

After having understood like terms, unlike terms and their difference, students have the question, "Why should we know the difference between like and unlike terms?" or "What is the use of knowing the difference between like terms and unlike terms?".

To do addition and subtraction of algebraic expression, we have to know the difference between like and unlike terms.

Because, in algebraic expression, we can do addition and subtraction only on like terms not on unlike terms.

We
hope, now the students would have understood the reason for why we
should know the difference between the like and unlike terms.

In the topic "Like and Unlike terms", next we are going to see how to add or subtract algebraic expressions when they have like terms.

Adding polynomials is nothing but combining the like terms. Here we give step by step explanation for adding polynomials.

Let us look at some examples to have better understanding on addition and subtraction of algebraic expression with like terms.

**Example 1 :**

**Add : 3x³ + x² - 2 and 2x² + 5x + 5**

**Solution : **

**We first arrange these two as follows and then add. **

**Observe the important points related to the above work. **

1. We have written the term 2x² of the second polynomial below the corresponding term x² of the first polynomial.

2. Similarly, the constant term +5 is placed below the constant term – 2.

3. Since the term x in the first polynomial and the term x³ in the second polynomial do not exist, their respective places have been left blank to facilitate the process of addition.Or, for the non existing terms, we annexe the terms with zero coefficients.

Let us look at the next example on "Like terms and unlike terms"

**Example 2 :**

**Find out the sum of the polynomials 3x - y, 2y - 2x, and x + y. **

**Solution : **

We can find out the sum of the given polynomials using either column method of addition or row method of addition as explained below.

**Let us look at the next example on "Like terms and unlike terms"**

**Example 3 :**

**Subtract 5xy from 8xy. **

**Solution : **

**Let us look at the next example on "Like terms and unlike terms"**

**Example 4 :**

**Subtract (3c + 7d****²) from (5c - d****²)**

**Solution : **

**Alternatively, this can also be done as :**

**( 5c - d² ) - ( 3c + 7d² ) = 5c - d² - 3c - 7d² **

**= ( 5c - 3c ) + ( -d² - 7d² )**

**= 2c + ( - 8d² )**

**= 2c - 8d²**

**Let us look at the next example on "Like terms and unlike terms"**

**Example 5 :**

**Subtract ( 2x****² + 2y****² - 6 ****) from ( 3x****² - 7y****² + 9 )**

**Solution : **

**Let us look at the next example on "Like terms and unlike terms"**

**Example 6 :**

**Add ( 7p³ + 4p²- 8p + 1 ) and (3p³- 5p²- 10p + 5)**

**Solution : **

**Step 1:**

**The two given polynomials are already in the arranged form.So we can leave it as it is.**

** = ( 7p³ + 4p²- 8p + 1) + (3p³ - 5p² - 10p + 5)**

**Step 2 :**

**Now we have to write the like terms together starting from the highest power to lowest power.**

** = 7p³ + 3p³ + 4p²- 5p²- 8p - 10p + 1 + 5**

**So the final answer is 10p³- 1p²- 18p + 6**

Let us look at the next example on "Like terms and unlike terms"

**Example 7 :**

**Add ( 2x³ + 5x² - 2x + 7 ) and ( x³ + 4x² - x + 6)**

**Solution : **

** = ( 2x³ + 5x² - 2x + 7 ) + ( x³ + 4x² - x + 6)**

** = 2x³ + 5x² - 2x + 7 + x³ + 4x² - x + 6**

** = 2x³ + x³ + 5x² + 4x² - 2x - x + 7 + 6**

** = 3x³ + 9x² - 3x + 13 **

Let us look at the next example on "Like terms and unlike terms"

**Example 8 :**

**Add ( 3x³ - 2x² - x + 4 ) and ( 2x³ + 7x² - 3x - 3 )**

**Solution : **

** = (3x³ - 2x² - x + 4) + (2x³ + 7x² - 3x - 3)**

** = 3 x³ - 2 x² - x + 4 + 2 x³ + 7 x² - 3 x - 3**

** = 3x³ + 2x³ - 2x² + 7x² - x - 3x + 4 - 3**

** = 5x³ + 5x² - 4x + 1 **

Let us look at the next example on "Like terms and unlike terms"

**Example 9 :**

** Add 2( x³ - x² + 6x - 2 ) and ( 5x⁶ + 7x⁵ - 3x - 3 )**

**Solution : **

** = 2( x³ - x² + 6 x - 2 ) + ( 5 x⁶ + 7 x⁵ - 3 x - 3 )**

** = 2x³ - 2x² + 12x - 4 + 5x⁶ + 7x⁵ - 3x - 3**

** = 5x⁶ + 7x⁵ + 2x³ - 2x² + 12x - 3x - 4 - 3**

** = 5x⁶ + 7x⁵ + 2x³ - 2x² + 9x - 7**

Let us look at the next example on "Like terms and unlike terms"

**Example 10 :**

** Add -1( x⁶ + x³ + 6x² - 2 ) and 2( 5x⁶ + 7x⁵ - 3x - 3 )**

**Solution : **

** = -1( x⁶ + x³ + 6x² - 2 ) + 2( 5x⁶ + 7x⁵ - 3x - 3 )**

** = -x⁶ - x³ - 6x² + 2 + 10x⁶ + 14x⁵ - 6x - 6**

** = -x⁶ + 10x⁶ + 14x⁵ - x³ - 6x² - 6x + 2 - 6**

** = 9x⁶ + 14x⁵ - x³ - 6x² - 6x - 4**

Let us look at the next example on "Like terms and unlike terms"

**Example 11 :**

**Add 5( 5x⁶ + 2x³ - 6x² - 2 ) + 6(-3x⁶ + 2x⁵ + 2x + 1 )**

**Solution : **

** = 5( 5x⁶ + 2x³ - 6x² - 2 ) + 6( -3x⁶ + 2x⁵ + 2x + 1 )**

** = 25x⁶ + 10x³ - 30x² - 10 -18x⁶ + 12x⁵ + 12x + 6**

** = 25x⁶ -18x⁶ + 12x⁵ + 10x³ - 30x² + 12x -10 + 6**

** = 7x⁶ + 12x⁵ + 10x³ - 30x² + 12x - 4**

Let us look at the next example on "Like terms and unlike terms"

**Example 12 :**

**Add -2 ( 2x⁴ - 2x³ - x² + 5 ) and 3 ( 2x⁴ - 2x² - 3 )**

**Solution :**

** = -2( 2x⁴ - 2x³ - x² + 5 ) + 3( 2x⁴ - 2x² - 3 )**

** = -4x⁴ + 4x³ + 2x² -10 + 6x⁴ - 6x² - 9**

** = -4x⁴ + 6x⁴ + 4x³ + 2x² - 6x² -10 - 9**

** = 2x⁴ + 4x³ - 4x² - 19**

Let us look at the next example on "Like terms and unlike terms"

**Example 13 :**

**Add 5( x⁴ - x³ + 5 ) and 2( x⁴ - 5x² - 7 )**

**Solution :**

** = 5( x⁴ - x³ + 5 ) + 2( x⁴ - 5x² - 7 )**

** = 5x⁴ - 5 x³ + 25 + 2x⁴ - 10x² - 14**

** = 5x⁴ + 2x⁴ - 5x³ - 10x² + 25 - 14**

** = 7x⁴ - 15x³ + 11**

Let us look at the next example on "Like and unlike terms"

**Example 14 : **

**Add 3( 6x⁴ - 2x³ - 3 ) and 2( 2x⁴ - x² - 8 )**

**Solution : **

** = 3 ( 6x⁴ - 2x³ - 3 ) + 2 ( 2x⁴ - x² - 8 )**

** = 18x⁴ - 6x³ - 9 + 4x⁴ -2x² - 16**

** = 18x⁴ + 4x⁴ - 6x³ -2x² - 9 - 16**

** = 22 x⁴ - 6x³ -2x² - 25**

Let us look at the next example on "Like terms and unlike terms"

**Example 15 :**

** Add (6x⁷-2x⁶-3x³+2x²) and 2(2x⁴+5x⁷+ 3x⁶+ x³+x²)**

**Solution : **

** = ( 6x⁷- 2x⁶- 3x³+ 2x²) + 2( 2x⁴ + 5x⁷ + 3x⁶ + x³ + x² )**

** = 6x⁷ - 2x⁶ - 3x³ + 2x² + 4x⁴ + 10x⁷ + 6x⁶ + 2x³ + 2x²**

** = 6x⁷ + 10x⁷- 2x⁶ + 6x⁶ + 4x⁴ - 3x³ + 2x³ + 2x² + 2x²**

** = 16x⁷ + 4x⁶ + 4x⁴ - x³ + 4x²**

Let us look at the next example on "Like and unlike terms"

**Example 16 :**

**Add (x⁷-3x⁶-2x³+x²) and 5 (3x⁴+15x⁷+4x⁶+2x³+6x²)**

**Solution : **

** = (x⁷-3x⁶-2x³+x²) + 5 (3x⁴ + 15x⁷ + 4x⁶ + 2x³+ 6x² )**

** = x⁷- 3x⁶ - 2x³ + x² + 15x⁴ + 75x⁷ + 20x⁶ + 10x³ + 30x²**

** = x⁷ + 75x⁷- 3x⁶ + 20x⁶ - 2x³ + 10x³ + x² + 30x²**

** = 76x⁷ + 17x⁶ + 8x³ + 31x²**

After having gone through the examples explained above, we hope that the students would have understood the stuff "Like and unlike terms"

After having gone through the stuff and example problems, we hope that the students would have understood like terms and unlike terms.

**Related topics :**

**Like fractions and unlike fractions **

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