Algebra Tutorials!
Monday 15th of July
 Home Rotating a Parabola Multiplying Fractions Finding Factors Miscellaneous Equations Mixed Numbers and Improper Fractions Systems of Equations in Two Variables Literal Numbers Adding and Subtracting Polynomials Subtracting Integers Simplifying Complex Fractions Decimals and Fractions Multiplying Integers Logarithmic Functions Multiplying Monomials Mixed The Square of a Binomial Factoring Trinomials The Pythagorean Theorem Solving Radical Equations in One Variable Multiplying Binomials Using the FOIL Method Imaginary Numbers Solving Quadratic Equations Using the Quadratic Formula Solving Quadratic Equations Algebra Order of Operations Dividing Complex Numbers Polynomials The Appearance of a Polynomial Equation Standard Form of a Line Positive Integral Divisors Dividing Fractions Solving Linear Systems of Equations by Elimination Factoring Multiplying and Dividing Square Roots Functions and Graphs Dividing Polynomials Solving Rational Equations Numbers Use of Parentheses or Brackets (The Distributive Law) Multiplying and Dividing by Monomials Solving Quadratic Equations by Graphing Multiplying Decimals Use of Parentheses or Brackets (The Distributive Law) Simplifying Complex Fractions 1 Adding Fractions Simplifying Complex Fractions Solutions to Linear Equations in Two Variables Quadratic Expressions Completing Squares Dividing Radical Expressions Rise and Run Graphing Exponential Functions Multiplying by a Monomial The Cartesian Coordinate System Writing the Terms of a Polynomial in Descending Order Fractions Polynomials Quadratic Expressions Solving Inequalities Solving Rational Inequalities with a Sign Graph Solving Linear Equations Solving an Equation with Two Radical Terms Simplifying Rational Expressions Exponents Intercepts of a Line Completing the Square Order of Operations Factoring Trinomials Solving Linear Equations Solving Multi-Step Inequalities Solving Quadratic Equations Graphically and Algebraically Collecting Like Terms Solving Equations with Radicals and Exponents Percent of Change Powers of ten (Scientific Notation) Comparing Integers on a Number Line Solving Systems of Equations Using Substitution Factoring Out the Greatest Common Factor Families of Functions Monomial Factors Multiplying and Dividing Complex Numbers Properties of Exponents Multiplying Square Roots Radicals Adding or Subtracting Rational Expressions with Different Denominators Expressions with Variables as Exponents The Quadratic Formula Writing a Quadratic with Given Solutions Simplifying Square Roots Adding and Subtracting Square Roots Adding and Subtracting Rational Expressions Combining Like Radical Terms Solving Systems of Equations Using Substitution Dividing Polynomials Graphing Functions Product of a Sum and a Difference Solving First Degree Inequalities Solving Equations with Radicals and Exponents Roots and Powers Multiplying Numbers
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Collecing Like Terms

Like terms in an algebraic expression are terms with identical symbolic or variable parts. Thus

‘3x’ and ‘7x‘ are like terms because both contain the symbolic part ‘x’

‘5x 2 yz’ and ‘13x 2 yz’ are like terms because both contain the symbolic part ‘x 2 yz’

‘4x 2 ’and ‘7x’ are not like terms because even though the symbol present in both is ‘x’, the symbolic part ‘x 2 ’ is not identical to the symbolic part ‘x’.

Algebraic expressions that contain like terms can be simplified by combining each group of like terms into a single term. The reason why this is possible and valid is quite easy to see. For instance, consider the expression

3x + 7x

which is the sum of two like terms, representing the accumulation of three x’s and another seven x’s. Clearly, the end result is a total of ten x’s. In notation

3x + 7x = (3 + 7)x = 10x

This process of combining (or collecting ) like terms can be performed for each group of like terms that appear in an expression. The net effect will be that the original expression can now be written with fewer terms, yet which are entirely equivalent to the terms in the original expression.

Example:

Simplify: 5x 2 + 9 – 3x + 4x 2 + 8x + 7.

solution:

This expression has six terms altogether. However, we notice that

• two of the terms have the literal part ‘x 2 ’ and so are like terms – we can replace

5x 2 + 4x 2 by (5 + 4)x 2 = 9x 2

two of the terms have the same literal part ‘x’ and so are also like terms. We can replace

-3x + 8x by (-3 + 8)x = 5x

two of the terms are just constants, and so obviously can be combined arithmetically:

9 + 7 = 16.

So

5x 2 + 9 – 3x + 4x 2 + 8x + 7

= 5x 2 + 4x 2 + (-3x) + 8x + 9 + 7

= (5 + 4)x 2 + (-3 + 8)x + 16

= 9x 2 + 5x + 16.

Thus, in simplest form, the original six term expression can be rewritten as

9x 2 + 5x + 16

consisting of just three terms.

 Copyrights © 2005-2024