I used to think that \(20^2 + 14^2\) is the same as \((20 + 14)^2.\) But I have seen that they are not the same. This is because, if I consider \(20^2 + 14^2\), I will get \(400 + 196 = 596.\) If I consider, \((20 + 14)^2\), I will get \((20+14)^2 = 34^2 = 1156\) So, why am I getting diferent results?
The closed brackets always are the thing done first. http://math.about.com/od/glossaryofterms/g/What-Is-Bedmas.htm
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Because if you multiply out pairs of brackets containing 2 terms, you multiply each term in one bracket by BOTH terms in the other one. For example: (a+b)(c+d) = ac + ad + bc + bd. So (20+14)(20+14) = 20x20 + 20x14 + 14x20 + 14x14. A generally useful schoolboy result is (a+b)² = a² + 2ab + b², as the above example illustrates. Which leads to another useful schoolboy result, which is that a² - b² = (a+b)(a-b), famously known as the "difference of two squares".
This is all about exponentiation. It is one of the basic principles taught in first-year algebra. American schools usually teach this in the 7th grade--when most students are approximately age 12. If you haven't had this class yet, be patient. When you have the opportunity to study algebra it will all begin to make sense. Of course if you don't feel like waiting, there's nothing stopping you from going to the library and checking out a book on elementary algebra. Please Register or Log in to view the hidden image!
Since you calculated them both correctly, you must know the answer to your own question Please Register or Log in to view the hidden image!
I think the best thing that will ever work for me here, is to ensure that I follow the order of operation. That is squaring has to be done first, before I could get the right thing. \((20 + 14)^2\) = 400+196 = 596.
If you feel like a technical answer, it is because exponentiation is not distributive over addition: http://en.wikipedia.org/wiki/Distributive_property
that is great chikis, you start of the thread doing it right and after all of the input you got; now you are doing it wrong. Just shoot me!
What I have said stands. Take a look at this http://en.m.wikipedia.org/wiki/Order_of_operations. The standard order of operations The order of operations used throughout mathematics, science, technology and many computer programming languages is expressed here:[2] exponents and roots multiplication and division addition and subtraction This means that if a mathematical expression is preceded by one binary operator and followed by another, the operator higher on the list should be applied first
no, squaring is not necessarily done first. beer w/straw had it right, items in parenthesis is done first. in your quote above: 14 is added to 20 to get 34, then the result is squared to get 1156.
No, that is not right. Try it with diffrence of two squares and you will see see reason in what am saying.
bi and trinomials should be done with careful process, pay attention is the key. but after it is understood, it does become easy to see. to be honest, you may not understand until you get into factoring tri's. also, differences of cubes might be just as confusing for some.
