anonymous
  • anonymous
Find a pair of factors for each number by using the difference of two squares. a. 45 b. 77 c. 112
Mathematics
chestercat
  • chestercat
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KingGeorge
  • KingGeorge
Let's start with a. Using difference of two squares, note that \(45=49-4=7^2-2^2\)This last expression can be factored easily as \[7^2-2^2=(7-2)\cdot(7+2)\]Hence, your factorization is \(9\cdot 5\)
KingGeorge
  • KingGeorge
For b, we want to write\[77=81-4=9^2-2^2\]Can you factorize from there?
anonymous
  • anonymous
trying to figure it out

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KingGeorge
  • KingGeorge
There's an easy way to factorize a difference of two squares. If you have a differnece of two squares \[a^2-b^2\]then this factors into\[a^2-b^2=(a-b)\cdot(a+b)\]Does this help?
anonymous
  • anonymous
no sorry
KingGeorge
  • KingGeorge
So you have an equation of the form \[a^2-b^2\]where \(a=9\) and \(b=2\). Thus, \[a^2-b^2=(a-b)\cdot(a+b)\]can be replaced by \[9^2-2^2=(9-2)\cdot(9+2)\]Which then simplifies to \[7\cdot11\]
KingGeorge
  • KingGeorge
Let's move on to c. We want to factor 112. Notice that \[112=121-9=11^2-3^2\]Using the same principles as above, can you try to factor this one?
anonymous
  • anonymous
i do not understand how u did this
KingGeorge
  • KingGeorge
Sorry, I had to go get dinner. What part of this do you now understand?
anonymous
  • anonymous
c. 8x14

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