AJ Spotlight on Precalculus
As a Precalculus tutor, I often encounter students who find the difference of cubes formula difficult to remember. While it seems like just another formula to memorize, understanding and using it effectively can boost their understanding and success in Precalculus class. Luckily, there’s a simple trick to make it easier: the mnemonic “SOAP.”
What is a Mnemonic Device?
A mnemonic device is when we take a set of steps of instructions and boil them down into a meaningful acronym. These are some of our tutors favorite tools for supporting students, and algebra tutors often use mnemonic devices to help reinforce foundational skills in problem-solving and factoring. Beginning math students learn about mnemonic devices when taught PEMDAS, or the order of operations. Below, we tackle the more advanced acronym SOAP
The Process of SOAP
The difference of cubes formula, a3–b3=(a-b)(a2+ab+b2), is a key tool in algebra that students frequently see in their precalculus course. Students use it for factoring expressions involving cubic terms. Gaining comfort with SOAP can improve their understanding of more advanced topics.
“SOAP” helps simplify the process of recalling the difference of cubes formula. “S” stands for “Same” sign in the first factor, (a-b), showing that the sign in this factor is the same as the original expression. “O” stands for “Opposite” sign in the second factor, (a2+ab+b2), meaning the sign of the middle term should be opposite to the original expression. Also, “A” and “P” stands for “Always Positive” for the last term in the second factor. While this concept is rooted in algebra, it also builds the kind of reasoning skills reinforced by a trigonometry tutor as students move into more advanced precalculus topics.
Students can easily remember and apply the difference of cubes formula by using “SOAP.” They can then apply the difference of cubes formula without getting intimidated by the details. “SOAP” provides a clear and effective way to remember the correct sign patterns, which makes the process of factoring cubic expressions more easier overall. Moreover, by working with an algebra tutor or precalculus tutor and utilizing effective tools and strategies in math, such as the “SOAP” mnemonic, students can continue to improve on their fundamental algebra skills.
Why Are Mnemonic Devices Effective?
Mnemonic devices are useful tools for easily remembering step by step directions to tasks and mathematical equations. From SOAP and PEMDAS, to remembering the steps to cook a specific dish, mnemonic devices have proven effective time and again! Interested in reading a study on mnemonic devices and their effectiveness? Click here!
Final Thoughts on Mastering Precalculus
By using simple strategies like the SOAP mnemonic and strengthening foundational skills with support from algebra tutors, students can better understand precalculus concepts and improve problem-solving confidence, especially with guidance from a precalculus tutor as they prepare for more advanced topics like those reinforced by a trigonometry tutor.
