anonymous
  • anonymous
Which binomial is a difference of squares? (Points : 1) 14x2 – 81 16x2 – 81 25x2 + 81 36x3 – 81
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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Elsa213
  • Elsa213
congrats on reaching ur 100th question :D
anonymous
  • anonymous
thank you!!
johnweldon1993
  • johnweldon1993
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?

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anonymous
  • anonymous
7
johnweldon1993
  • johnweldon1993
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
johnweldon1993
  • johnweldon1993
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...
johnweldon1993
  • johnweldon1993
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
johnweldon1993
  • johnweldon1993
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
anonymous
  • anonymous
ok thank you!
johnweldon1993
  • johnweldon1993
Did that at least make sense? Lol, but no problem :)
anonymous
  • anonymous
YES IT DID
johnweldon1993
  • johnweldon1993
Okay good :)

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