Algebra Tutorials!  
Monday 15th of July
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
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
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
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
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
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
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
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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.


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


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.


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.


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