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Math Help - Expanding Expressions Qustions

  1. #1
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    Question Expanding Expressions Qustions

    Hi guys not sure how to approach these questions would appreciate being pointed in the right direction

    Question:

    Expand the following expressions, collecting together like terms where possible;

    1. (ax + b) ^2

    2. 4(x/2 - 3 ) (7y - x)

    Thanks in advance
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  2. #2
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    1. To square an expression means to multiply that expression by itself. So this is equal to (ax+b)(ax+b). Can you FOIL this expression?

    2. Leave the 4 outside, and FOIL the two binomials. Give it a shot and let's see how you do.
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  3. #3
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    Quote Originally Posted by DrSteve View Post
    1. To square an expression means to multiply that expression by itself. So this is equal to (ax+b)(ax+b). Can you FOIL this expression?

    2. Leave the 4 outside, and FOIL the two binomials. Give it a shot and let's see how you do.
    Thanks for the quick response Steve

    I'm not familliar with the term FOIL are you possibly refering to multiplying the brackets out?

    Thanks
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  4. #4
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    Quote Originally Posted by komodo View Post
    Thanks for the quick response Steve

    I'm not familliar with the term FOIL are you possibly refering to multiplying the brackets out?

    Thanks
    Yes. FOIL is a mnemonic i think it's called. Multiplying the brackets out is the same thing as expanding an expression, so do that.
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  5. #5
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    I think I understand that I have multiply the First, Outter, Inner and Last in that order then collect like terms hence FOIL.

    Can someone give me the answers so I can check if I've done it correctly

    Thanks guys
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  6. #6
    Super Member Quacky's Avatar
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    Quote Originally Posted by komodo View Post
    I think I understand that I have multiply the First, Outter, Inner and Last in that order then collect like terms hence FOIL.

    Can someone give me the answers so I can check if I've done it correctly

    Thanks guys
    Post your answers, and we'll tell you if you're correct.
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  7. #7
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    Quote Originally Posted by Quacky View Post
    Post your answers, and we'll tell you if you're correct.
    This is what I got for the 1st one not sure if I've done it correctly though....

    (ax + b) ^2

    = (ax + b) (ax + b)

    = (2ax + axb) (axb + b^2)

    = 2ax + 2axb + b^2

    Is this correct feels like I've done something wrong
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  8. #8
    Super Member Quacky's Avatar
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    Quote Originally Posted by komodo View Post
    This is what I got for the 1st one not sure if I've done it correctly though....

    (ax + b) ^2

    = (ax + b) (ax + b)

    = (2ax + axb) (axb + b^2)

    = 2ax + 2axb + b^2

    Is this correct feels like I've done something wrong
    Just some silly errors. If I have ax\times ax then this is a\times a\times x\times x (because the order of multiplication doesn't matter) which is the same as a^2x^2 So this is the change you need to make:

    a^2x^2 + axb + axb + b^2 (don't use brackets for addition!)

    =a^2x^2+2axb+b^2

    Otherwise, it's fine. Be careful with how you set your work out, try and follow my example above for the second problem, and just be cautious where you put brackets (implying multiplication) and plus signs (obviously for addition).
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  9. #9
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    Quote Originally Posted by Quacky View Post
    Just some silly errors. If I have ax\times ax then this is a\times a\times x\times x (because the order of multiplication doesn't matter) which is the same as a^2x^2 So this is the change you need to make:

    a^2x^2 + axb + axb + b^2 (don't use brackets for addition!)

    =a^2x^2+2axb+b^2
    Thanks for the advice it was a pretty stupid mistake....the 2nd expression is also proving kind of tricky its different to all the previous exercises that I've attempted prior but here is a long shot at it:

    4 (x/2 - 3) (7y - x)

    = 4 (x/2.7y - x^2/2 - 21y - 3x)

    Dont know whether to multiply everything in the brackets by the 4 outside or even if whats in the brackets is correct...help would be much appreciated
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  10. #10
    Super Member Quacky's Avatar
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    Quote Originally Posted by komodo View Post
    Thanks for the advice it was a pretty stupid mistake....the 2nd expression is also proving kind of tricky its different to all the previous exercises that I've attempted prior but here is a long shot at it:

    4 (x/2 - 3) (7y - x)

    = 4 (x/2.7y - x^2/2 - 21y - 3x)

    Dont know whether to multiply everything in the brackets by the 4 outside or even if whats in the brackets is correct...help would be much appreciated
    Yeah, you want to multiply everything inside by 4. You've made a slight sign error:

    = 4 (x/2.7y - x^2/2 - 21y + 3x) Remember that two negatives make a positive!

    Finish up by multiplying through by four.
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  11. #11
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    Quote Originally Posted by Quacky View Post
    Yeah, you want to multiply everything inside by 4. You've made a slight sign error:

    = 4 (x/2.7y - x^2/2 - 21y + 3x) Remember that two negatives make a positive!

    Finish up by multiplying through by four.
    In that case I have :

    4x/2.7y - 4x^2/2 - 84y + 12x (Personaly I cant see any like terms to collect)

    Is this more like it?
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  12. #12
    Super Member Quacky's Avatar
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    Quote Originally Posted by komodo View Post
    In that case I have :

    4x/2.7y - 4x^2/2 - 84y + 12x (Personaly I cant see any like terms to collect)

    Is this more like it?
    Some of your terms are a mess. Remember that multiplication/division are (generally) commutative, meaning they can be done in any order. Your first term there is \frac{4\times 7 \times x\times y}{2} which can be simplified to just 14xy

    Similarly, \frac{4x^2}{2}=2x^2
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  13. #13
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    Quote Originally Posted by Quacky View Post
    Some of your terms are a mess. Remember that multiplication/division are (generally) commutative, meaning they can be done in any order. Your first term there is \frac{4\times 7 \times x\times y}{2} which can be simplified to just 14xy

    Similarly, \frac{4x^2}{2}=2x^2
    Now its starting to make sence wasn't aware that I could do that....therefore I should end up with:

    14xy - 2x^2 - 84y + 12x
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  14. #14
    Super Member Quacky's Avatar
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    Quote Originally Posted by komodo View Post
    Now its starting to make sence wasn't aware that I could do that....therefore I should end up with:

    14xy - 2x^2 - 84y + 12x
    There we go .
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  15. #15
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    Quote Originally Posted by Quacky View Post
    There we go .
    Thats right lol.......I'm loosing sleep over this stuff

    Anyway thanks for help realy appreciate it
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