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Sunday, September 30, 2012

Multiplying Polynomials

Category: Algebra

"Published in Newark, California, USA"

Perform the indicated operations for
 
 
Solution:
 
The above equation is a multiplication of a binomial with a trinomial. Let's apply the Distributive Law for the above equation as follows
 
 
 
Then apply the Laws of Exponents for the above equation as follows
 
 
 
 
Therefore, the answer is
 


Saturday, September 29, 2012

Adding - Subtracting Polynomials

Category: Algebra

"Published in Newark, California, USA"

Add the following polynomials:


Solution:

The first thing that we have to do to is to arrange the given polynomials as follows

 
Since all the grouped terms are all addition, then we can add all the same terms. If it is subtraction of polynomials, then we have to change the sign of the terms of the subtrahend first and then perform the addition. Now, let's combine the same terms and variables of the polynomials as follows




Therefore, the answer is 0.

Note: When you do any algebraic operations, please be very careful because many students are sometimes make a mistake especially with the signs. 

Friday, September 28, 2012

Factoring - Perfect Trinomial Square

Category: Algebra

"Published in Newark, California, USA"

Find the factors of  .
 

Solution:
 
Examine first the given trinomial if there are any common factor or not. In this case, their common factor is 2. Remove their common factor, we have



     
Since the result of a trinomial is a perfect square, therefore 



Check:      

How do you know if the given trinomial is a perfect square or not? Here's the technique


Therefore, the middle term is