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Wednesday, November 6, 2013

Special Products - Factoring, 26

Category: Algebra

"Published in Newark, California, USA"

Find the factors for


Solution:

Consider the given equation above


Did you notice that the given equation is a quadratic equation of variable y? The coefficient of three terms are also variables. In this type of quadratic equation, we have to do the trial and error method in factoring until we get the desired middle term. The coefficient of y² can be factored into (x + 1)(x - 1) while x² into x•x. Let's start the factoring of the given equation as follows



The middle term is




Since the value of the above calculation is the same as the middle term of the given equation which is -2xy, then the factors of the given equation are 

 

Tuesday, November 5, 2013

Special Products - Factoring, 25

Category: Algebra

"Published in Newark, California, USA"

Find the factors for


Solution:

Consider the given equation above


Did you notice that the given equation is a quadratic equation of variable x? The coefficient of three terms are also variables. In this type of quadratic equation, we have to do the trial and error method in factoring until we get the desired middle term. Since the coefficient of variables are already factored, then we can start to factor the given equation as follows



The middle term is 





Since the value of the above calculation is the same as the middle term of the given equation which is 4x, then the factors of the given equation are

 

Monday, November 4, 2013

Special Products - Factoring, 24

Category: Algebra

"Published in Suisun City, California, USA"

Find the factors for


Solution:

Consider the given equation above


Did you notice that the first three terms of the given equation is a perfect trinomial square? Well, let's group the first three terms as follows



At the last three terms, when you group and take out their negative sign, then it will be a perfect trinomial square, too as follows
 
  

Next, rewrite the grouped terms in terms of exponential function as follows
 
 
 
Since the above equation can be factored by the difference of two squares in which the grouped terms are considered as a single term, then the factors of the given equation are