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Exercises on Simplifying algebraic expressions by Combining Like Terms

This is a set of solved exercises on simplifying algebraic expressions by combining like terms. All you have to do is try to solve these exercises and compare your answers with the answers suggested by us.
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Exercise1:

Simplify the follwing expressions by combining like terms::

Solution:

  1. and are like terms. So, we can combine them:
  1. and are like terms. So, we can combine them:
  1. and are like terms. So, we can combine them:
  1. and are like terms. So, we can combine them:
  1. and are like terms. So, we can combine them. Also, and are like terms and we can combine them:
  1. and are like terms. So, we can combine them:
  1. and are like terms. So, we can combine them:
  1. and are like terms. So, we can combine them. Also, and are like terms and we can combine them:
  1. We can combine the term with the terms and , and combine the term with the terms and :
  1. and are like terms,
    and are like terms,
    and are like terms and additive inverse. So,

Exercise2:

Remove the symbols of grouping and simplify the resulting expressions by combining like terms:

Solution:

Remember this rules:

Note:

  1. If a sign precedes a symbol of grouping, this symbol of grouping may be removed without affecting the terms contained.
  2. If a sign precedes a symbol of grouping, this symbol of grouping may be removed if each sign of the terms contained is changed.
  3. If more than one symbol of grouping is present, the inner ones are to be removed first.

  1. Removing the symbols of grouping and simplifying the expresseion :

  2. Removing the symbols of grouping, applying the distributive properties and simplifying the expresseion :

  3. Removing the symbols of grouping, applying the distributive properties and simplifying the expresseion :

  4. Removing the symbols of grouping, applying the distributive properties and simplifying the expresseion :