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Expand and simplify this formula

  1. Feb 16, 2010 #1
    I had to expand and simplify this formula and I got it wrong.
    2a + 2 (3a + 2)
    I first multiplied the 2a by everything inside the bracket, giving:
    6a squared + 4a
    Then multiplied the 2 by everything inside the bracket, giving:
    6a + 4
    so in total I had:
    6a squared + 4a + 6a + 4
    which I simplified to:
    6a squared + 10a + 4

    The answer is actually:
    8a + 4
    Where did I go wrong?
     
  2. jcsd
  3. Feb 16, 2010 #2

    danago

    User Avatar
    Gold Member

    The problem is in your first step. The bracket is multiplied by just 2, not 2a.

    Your method would have been ok if the question was instead (2a + 2) (3a + 2). Note the extra set of brackets? It makes a big difference.

    Without the first set of brackets, the expression is essentially saying: "Evaluate '3a+2', multiply this by 2 and then add 2a".
    With the first set of brackets, the expression is saying: "Evaluate '3a+2', then evaluate '2a+2', and then multiply these two numbers".
     
  4. Feb 16, 2010 #3
    you first multiply the 2 by everything inside the bracket then it will give you correct ...
     
  5. Feb 16, 2010 #4
    Thank a lot Danago!
    So as a rule is it true to say that you only multiply everything inside the bracket only by the unit that comes immediately before the bracket? In the case 2?

    I got the following 2 questions right, and yet I multiplied everything inside the bracket by everything outside of it. What is the difference?

    4(3b - 2) - 5b
    ans - 7b -8

    6(2c - 1) - 7c
    ans - 5c -6
     
  6. Feb 16, 2010 #5
    The question you were confused on can be rewritten as 2(3+2a) + 2a, which is the same format as your other problems. See how this is different than what you originally solved, which was (2+2a)(3+2a)?
     
  7. Feb 16, 2010 #6
    kind of, just remember you dont multiply by something you're adding i.e.

    3a+a(6-2a)=9a-2a^2
    NOT
    18a^2-6a^3 do you follow?
     
  8. Feb 16, 2010 #7

    Mark44

    Staff: Mentor

    Gringo123,
    Something that you seem to be struggling with is the order of operations. You might not be aware that some arithmetic operations are more highly privileged than other.

    For example, the 2*3 + 5 simplifies to 11. The multiplication takes precedence over the addition, so this is evaluated as 6 + 5 rather that 2*8. The idea of operator precedence also applies to computer programming languages, in case your studies ever take you in that direction.

    Back when I was taking algebra years ago, my teach gave us a mnemonic device "My Dear Aunt Sally." The M and D represent multiplication and division; the A and S represent addition and subtraction. The idea is that multiplication or division always take precedence over addition or subtraction.

    If you need to change the order of operations, use parentheses () or brackets [] or braces {}.

    In your first post, you had 2a + 2 (3a + 2) and got the wrong answer. This is because you misinterpreted the problem as (2a + 2)(3a + 2), which it isn't.

    2a + 2 (3a + 2)
    = 2a + 6a + 4
    = 8a + 4
    You have to do the multiplication first - 2 times (3a + 2)
    Then you add 2a and the results of the previous step.
     
  9. Feb 16, 2010 #8
    Just to add on a tid bit, Please Excuse My Dear Aunt Sally is a little bit better--Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
     
  10. Feb 16, 2010 #9

    Mark44

    Staff: Mentor

    When I was learning algebra they hadn't invented exponents or parentheses yet:smile:
     
  11. Feb 16, 2010 #10

    Mentallic

    User Avatar
    Homework Helper

    Except you would've still learnt logarithms? :smile:

    And what about factorizing!?
     
  12. Feb 16, 2010 #11

    Mark44

    Staff: Mentor

    No, they didn't have them either.:cry:
     
  13. Feb 17, 2010 #12

    Mentallic

    User Avatar
    Homework Helper

    What an age to be living in... :bugeye:
     
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