Maharashtra State BoardSSC (English Medium) 7th Standard
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Subtraction of Algebraic Expressions

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Subtraction of Algebraic Expressions:

1. Subtraction of Like Terms:

  • If we have to subtract like terms then we can simply subtract their numerical coefficients.
  • The difference between two like terms is a like term with a numerical coefficient equal to the difference between the numerical coefficients of the two like terms.
  • Example: 11mn – 5mn = (11 – 5)mn = 6mn.

2. Subtraction of Unlike Terms:

  • If we have to subtract the unlike terms then we just have to put a minus sign between the terms.
  • Unlike terms cannot be subtracted the way like terms are subtracted means unlike term left as they are.
  • Example: 3xy – 7.

Subtraction of General Algebraic Expression:

Horizontal Steps:

  1. To subtract the general algebraic expressions, we have to arrange them so that the like terms come together, then simplify the terms, and the unlike terms will remain the same in the resultant expression.
  2. Subtract them as we subtract other numbers.

  3. If any term of the same variable is not there in another expression then write is as it is in the solution.

  4. Subtract 24ab – 10b – 18a from 30ab + 12b + 14a

    = 30ab + 12b + 14a – (24ab – 10b – 18a)

    = 30ab + 12b + 14a – 24ab + 10b + 18a

    = 30ab – 24ab + 12b + 10b + 14a + 18a

    = 6ab + 22b + 32a.

Vertical Steps:

  1. We write each expression to be subtracted in a separate row. While doing so we write like terms one below the other.
  2. Subtract them as we subtract other numbers.

  3. If any term of the same variable is not there in another expression then write is as it is in the solution.

  4. The signs in the third row written below each term in the second row help us in knowing which operation has to be performed.

  5. Subtraction of a number is the same as the addition of its additive inverse. Thus subtracting – 6 is the same as adding + 6.

  6. Subtract 24ab – 10b – 18a from 30ab + 12b + 14a.
  30ab + 12b + 14a
- 24ab - 10b - 18a
  - +   +  
  6ab + 22b + 32a

Example

Subtract 5x2 – 4y2 + 6y – 3 from 7x2 – 4xy + 8y2 + 5x – 3y.
  7x2 - 4xy + 8y2 + 5x  - 3y    
- 5x2     - 4y2     + 6y - 3
  (-)     (+)       (-)   (+)  
  2x2 - 4xy + 12y2 + 5x - 9y + 3
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