Welcome to my first lesson on mathematics tutoring. Today I am going to talk about ways in which you can handle algebra without struggling.
1. Learning how to expand “squared brackets” > (a +/- b) easily.
2. Learning how to manipulate squared brackets without expansion by using the concept of the “difference of two
squares”- (a + b)(a – b) and “squared brackets” > (a +/- b)^2
3. Learning how to save time by plugging sensible values.
Let us learn how to expand “squared brackets” easily. First of all you must be able to identify a “squared bracket”. A “square bracket appears in the form …..(a – b)^2 or (a + b)^2. To expand this easily…without doing it the long tiring way like:
(a – b)(a – b) = a^2 – ab –ba + b^2
= a^2 – 2ab + b^2
You may not think it is long to do but in the S.A.T. they use large numbers. Sometimes students make mistakes with the signs especially the one that comes before b^2.
To avoid this learn my technique I used. Some students may very well know this already but I am also here to help students who are weak in algebra.
When handling “squared brackets” always remember this format. Firstly square the first number, (a) becomes (a^2). Secondly multiply the first number (a) and last number (b) then multiply the resulting product by (- 2) if the sum is (a – b)^2 or by (2) if the sum is (a + b)^2. Lastly square the last number, (b) becomes (b^2). After all this is done, add all three steps together so that:
(a – b)^2 = a^2 – 2ab + b^2 and
(a + b)^2 = a^2 + 2ab + b^2
Wasn’t that simple? It looks complicated at first but with a few practice you can store it in long term memory. Okay, this was the first topic on my lesson. Let’s move on to topic 2.
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