# (Solution) Math114N Week 3 Discussion: Special Factoring Strategies

Required Resources

Read/review the following resources for this activity:

• Lesson in Canvas
• Assignments in Knewton
• Factoring Trinomials with a Leading Coefficient of 1
• Factoring Trinomials with a Leading Coefficient Other than 1
• Factoring Special Products
• Choosing a Factoring Strategy
• Solving Quadratic Equations by Factoring
• Solving Polynomial Equations by Factoring

Initial Post Instructions

This week we continue our study of factoring. As you become more familiar with factoring, you will notice there are some special factoring problems that follow specific patterns. These patterns are known as:

• a difference of squares;
• a perfect square trinomial;
• a difference of cubes; and
• a sum of cubes.

Choose two of the forms above and explain the pattern that allows you to recognize the binomial or trinomial as having special factors. Illustrate with examples of a binomial or trinomial expression that may be factored using the special techniques you are explaining. Make sure that you do not use the same example a classmate has already used!

Solution:

Two terms in a binomial that are perfect squares separated by a subtraction sign are referred to as difference of squares. An important note to remember: if subtraction separates two squared terms, then the sum and the difference of the two square roots factor the binomial. The formula follows: (a2-b2) = (a+b)(a-b). An example of a difference of squares equation is 9x2-16. The first step is to find the square root of both terms. The square root of 9x2 is 3x and the square root of 16 is 4. Now that we have determined that a=3x and b=4, we can plug in the numbers into the formula: (9x2-42) = (3x+4)(3x-4)…Please click the icon below to purchase full answer at only \$5