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anonymous

  • one year ago

Which binomial is a difference of squares? (Points : 1) 14x2 – 81 16x2 – 81 25x2 + 81 36x3 – 81

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  1. Elsa213
    • one year ago
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    congrats on reaching ur 100th question :D

  2. anonymous
    • one year ago
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    thank you!!

  3. johnweldon1993
    • one year ago
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    So a difference of squares we can write as \(\large a^2 - b^2\) Lets look at the first option for an example \[\large 14x^2 - 81\] Now we need to make that look like \(\large a^2 - b^2\) Well we know 81 = 9^2....but now what about 14? can that be written as something^2?

  4. anonymous
    • one year ago
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    7

  5. johnweldon1993
    • one year ago
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    Hmm lets test that...7^2 = 49 ....so not quite :) So since 14 cannot be written as a number^2 ....then this can NOT be a difference of squares

  6. johnweldon1993
    • one year ago
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    I hope that made sense? We basically want perfect squares to work with 1^2 = 1 2^2 = 4 3^2 = 9 4^2 = 16 5^2 = 25 etc...

  7. johnweldon1993
    • one year ago
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    So now lets move on to the third choice \[\large 25x^2 + 81\] Now notice...25 can be written as 5^2....so thats okay and notice 81 can be written as 9^2 So we have \[\large (5x)^2 \color\red{+} (9^2)\] Now....this WOULD be perfect...except this is a SUM of squares...not a DIFFERENCE of squares

  8. johnweldon1993
    • one year ago
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    And now what about the second choice? \[\large 16x^2 - 81\] Since 16 can be written as 4^2....and 81 can be written as 9^2...we could write \[\large (4x)^2 \color\red{-} (9)^2\] And that is indeed a DIFFERENCE of squares (the minus sign) so our answer here would be B

  9. anonymous
    • one year ago
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    ok thank you!

  10. johnweldon1993
    • one year ago
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    Did that at least make sense? Lol, but no problem :)

  11. anonymous
    • one year ago
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    YES IT DID

  12. johnweldon1993
    • one year ago
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    Okay good :)

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