Operations on Algebraic Expressions

Addition of algebraic expressions
To add algebraic expressions, rearrange the terms in the sum of the given algebraic expressions, so that their like terms and constants are grouped together. While rearranging terms, move them with the correct plus (+) or minus (–) sign before them.

To add like terms in an algebraic expression, multiply the sum of their coefficients with their common algebraic factors.
e.g. Add 5x2y + 6 and 2x2y – 11.
Sol: (5x2y + 6) + (2x2y – 11)
     = 5x2y +  6 + 2x2y – 11
     =  5x2y + 2x2y + 6 – 11
     = (5 + 2)x2y + 6 – 11
     = 7x2y – 5.

Subtraction of algebraic expressions
To subtract algebraic expressions

  • Change the signs of the terms of the expression being subtracted.
  • Rearrange the terms in the difference of the given algebraic expressions, so that their like terms and  constants are grouped together.
  • While rearranging terms, move them with the correct signs before them.
  • Multiply the difference of their coefficients with their common algebraic factors.
  • Unlike terms remain unchanged in the sum or difference of algebraic expressions.

         e.g. Subtract 2xy – 3x 2y – 4 from 2x2y – 3xy + 4y + 5.
               = (2x2y – 3xy + 4y + 5) – (2xy – 3x2y – 4)
               = 2x2y – 3xy + 4y + 5 – 2xy + 3x2y + 4
               = 2x2 y + 3x2y – 3xy – 2xy + 4y + 5 + 4
               = (2 + 3)x2y – 3xy – 2xy + 4y + 5 + 4
               = 5x2 y – 5xy + 4y + 9.

Summary

Addition of algebraic expressions
To add algebraic expressions, rearrange the terms in the sum of the given algebraic expressions, so that their like terms and constants are grouped together. While rearranging terms, move them with the correct plus (+) or minus (–) sign before them.

To add like terms in an algebraic expression, multiply the sum of their coefficients with their common algebraic factors.
e.g. Add 5x2y + 6 and 2x2y – 11.
Sol: (5x2y + 6) + (2x2y – 11)
     = 5x2y +  6 + 2x2y – 11
     =  5x2y + 2x2y + 6 – 11
     = (5 + 2)x2y + 6 – 11
     = 7x2y – 5.

Subtraction of algebraic expressions
To subtract algebraic expressions

  • Change the signs of the terms of the expression being subtracted.
  • Rearrange the terms in the difference of the given algebraic expressions, so that their like terms and  constants are grouped together.
  • While rearranging terms, move them with the correct signs before them.
  • Multiply the difference of their coefficients with their common algebraic factors.
  • Unlike terms remain unchanged in the sum or difference of algebraic expressions.

         e.g. Subtract 2xy – 3x 2y – 4 from 2x2y – 3xy + 4y + 5.
               = (2x2y – 3xy + 4y + 5) – (2xy – 3x2y – 4)
               = 2x2y – 3xy + 4y + 5 – 2xy + 3x2y + 4
               = 2x2 y + 3x2y – 3xy – 2xy + 4y + 5 + 4
               = (2 + 3)x2y – 3xy – 2xy + 4y + 5 + 4
               = 5x2 y – 5xy + 4y + 9.

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