Intermediate Algebra: One Step at a Time 

Pages 126 - 130:   #2, 10, 11, 18, 24, 28, 30, 32, 33, 34

Dr. Robert J. Rapalje

Seminole State College of Florida

Sanford, FL  32773

To see Section 2.01, with explanations, examples, exercises, and answers, click here!

p. 127.  # 2.        

Solution: 

Next, notice that this is a difference of two cubes!  The  FIRST is  and the SECOND is which can be written  .  Remember also that the difference of two cubes factors into the product of a binomial times a trinomial in this form, according to the formula . 

What you have is:

The trinomial CANNOT be factored, so this is your final answer!!

p. 127.  # 10.        

Next, notice that this is a difference of two cubes!  The  FIRST is  which can be written  and the SECOND is which can be written  .  Remember also that the difference of two cubes factors into the product of a binomial times a trinomial in this form, according to the formula . 

p. 128.  # 18.        

Solution: 

The first step is to recognize that there is a common factor.  Take out the 3 that is common to both terms.

Next, notice that what is left the parentheses is a difference of two cubes!  The  FIRST is  and the SECOND is which can be written  .  Remember also that the difference of two cubes factors into the product of a binomial times a trinomial in this form, according to the formula . 

What you have is:

The trinomial CANNOT be factored, so again this is your final answer!!

p. 130.  # 28.        

Solution:   

The first step is to recognize that there is a common factor.  Take out the 5 and the x factor that are common to both terms.

Next, notice that what is left the parentheses is a difference of two cubes! 

The  FIRST is  which can be written as  and

the SECOND is which can be written  . 

Remember also that the difference of two cubes is a binomial times a trinomial according to the formula . 

p. 130.  # 30.        

Solution:   

As always, the first step is to recognize that there is a common factor.  Take out the 25 and the  factor that are common to both terms.

Next, notice that what is left the parentheses is a sum of two cubes! 

The  FIRST is  which can be written as  and

the SECOND is which can be written  . 

Remember also that the sum of two cubes is a binomial times a trinomial according to the formula . 

p. 130.  # 32.        

Solution: 

In this case, there are NO common factors.  So, try a trinomial.  Notice that there are three terms, so it IS a trinomial, which can be factored into the product of two binomials.

Notice that each of these binomials are actually differences of two cubes, and each factors:

p. 130.  # 34.        

Solution: 

This problem is easiest to factor as a difference of two squares:

Notice that each of these binomials are actually difference and also sum of two cubes:

You finish it:

   Return to main page     Return to Intermediate Algebra      Math in Living C O L O R !!