The rules of addition of like terms are:

Rule I: When all the terms are positive, add their coefficients, also the variables and power of the like terms remains the same.

Examples:

1. 5xy, 4xy and xy.

Here, 5xy, 4xy and xy are like terms

The sum of the coefficients = 5 + 4 + 1 [xy means 1xy]

Therefore, 5xy + 4xy + xy = 10xy

Note:

To add two or more like terms, we add the numerical coefficients of the given terms and form another like term with the sum obtained as the numerical coefficient of the resulting term.

2. 5x + 4x + 2y + 3y

Here, 2x and 3x are like terms

and also 6y and 5y are like terms

5x + 4x = 9x

2y + 3y = 5y

Therefore, the answer is 9x + 5y

3. 3x3 + 7x3 + 4y2 + 7y2

Here, 3x3 + 7x3 are like terms

And also 4y2 + 7y2 are like terms

3x3 + 7x3 = 10x3

4y2 + 7y2 = 11y2

Therefore, the answer is 10x3 + 11y2

Rule II: When all the terms are negative, add their coefficient without considering their negative signs and then prefix the minus sign (-) to the sum.

Examples:

1. -3ab, -5ab and -ab

Without considering the negative signs, the coefficients of the given terms are 3, 5 and 1 respectively; and 3 + 5 + 1 = 9.

Therefore, addition of -3ab, -5ab and –ab = -9ab

i.e. (-3ab) + (-5ab) + (-ab) = -9ab

2. -5x + (-4x) + (-2y) + (-3y)

Here, -5x and -4x are like terms

and also -2y and -5y are like terms

(-5x) + (-4x) = -9x

(-2y) + (-3y) = -5y

Therefore, the answer is -9x - 5y.

Rule III: When all the terms are not of same sign. The same rule as that for the addition of integers should be applied.

Examples:

1. Addition of 21m and –9m

= 21m + (-9m)

= 21m - 9m

= m(21 - 9)

= 12m

2. 9xy – 4xy – 5xy + 7xy – xy

= 5xy – 5xy + 7xy – xy

= 0 + 7xy – xy, [since, 5xy – 5xy = 0]

= 6xy.

Like Terms

Subtraction of Like Terms

Unlike Terms

Subtraction of Unlike Terms

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Shifting of Digits in a Number |Exchanging the Digits to Another Place

May 19, 24 06:35 PM

What is the Effect of shifting of digits in a number? Let us observe two numbers 1528 and 5182. We see that the digits are the same, but places are different in these two numbers. Thus, if the digits…

2. ### Formation of Greatest and Smallest Numbers | Arranging the Numbers

May 19, 24 03:36 PM

the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number…

3. ### Formation of Numbers with the Given Digits |Making Numbers with Digits

May 19, 24 03:19 PM

In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits.

4. ### Arranging Numbers | Ascending Order | Descending Order |Compare Digits

May 19, 24 02:23 PM

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…

5. ### Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

May 19, 24 01:26 PM

Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits…