There are 3 types of algebra questions.
Expand and simplify
Factorize
Solve
Most students struggle in different aspects of algebra. For those who don't and claim to understand, some might end up going in circles rather than answering the question. One of my students once shared with me how a classmate of his was supposed to expand and simplify. However, after simplification, he went to factorize the equation and was left wondering why he got the initial expression as the answer.
For sec 2 math, students tend to answer questions based on body memory rather than actually understanding the requirement of the question. Hence, it is incredibly important to identify the type of question asked of you and the appropriate technique to apply.
In this article, we will examine the 3 algebra identities that you need to know.
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Table of content
1. How to apply
All algebra identities require one simple technique. Comparison.
When presented with an expression, sec 2 math students are to compare the given expression with all the identities they have been taught. They are to then decide upon the appropriate algebra identity to superimpose on, and substitute the appropriate variable before expanding further and simplifying.
The steps are essentially
Identify
Apply
Compare & Substitute
Simplify
These steps are illustrated in my TikTok videos and briefly explained in this article.
2. (a+b)^2
This is the easiest identity to apply. As long as a student sees a 'plus' sign within the bracket, this identity can be used. It can also be used when a 'minus' sign is within the bracket. However, the student is to be aware that the 'b' variable would include the negative sign from the term you compared it with.
3. (a-b)^2
For some this identity would seem redundant. For others, they may see this as a source of confusion. In order to apply this identity, the student is to identify the 'minus' sign within the bracket. The confusion comes when students are unsure as to whether the 'minus' sign from the term that you compared to is to be included when substituted into the equation.
No, do not include the 'minus' or negative sign. The negative sign has already been accounted for by the identity and hence, the inclusion would only double count for the negative sign resulting in the wrong answer. If this confuses you, just apply the addition identity and include the negative sign together.
3. Difference of Squares
This identity is the easiest to recognize for most students. This is the only identity that involves 2 pairs of brackets with 2 similar yet different variables. The difference is the sign. One of the variables would be identical whereas the other is the same variable albeit with a different sign. Upon expansion, the expression would be of 2 terms that have been squared accompanied with a 'minus' sign. In other words, upon expansion, you would get the difference between the 2 terms which has been squared. Hence, the name difference of squares.
Expansion is easy
Many sec 2 math students find algebra expansion the easiest to score, especially when it concerns identities. Expansion questions are usually mechanical and can be simplified even without the use of identities.
Few struggle for them, it is usually down to the lack of practice. Regardless of why you might struggle with algebra, you may always contact us for a trial lesson. We, at VANTAGE TUTOR, are patient and reliable. Our Math and Physics tutors have helped countless students improve their grades and achieve their academic goals in various subjects.
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