Addition of Like Terms

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.

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● Terms

Like and Unlike Terms

Like Terms

Addition of Like Terms

Subtraction of Like Terms

Adding and Subtracting Like Terms

Unlike Terms

Addition of Unlike Terms

Subtraction of Unlike Terms

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