anonymous
  • anonymous
Factor: x2 - 100
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Vocaloid
  • Vocaloid
hint: (A^2-B^2) = (A+B)(A-B) x^2 - 100 = ?
SolomonZelman
  • SolomonZelman
yes, and `100=10²` as you probably know already.
UsukiDoll
  • UsukiDoll
difference of squares formula \[(a^2-b^2)=(a+b)(a-b) \]

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More answers

anonymous
  • anonymous
is it 1000? IDK
SolomonZelman
  • SolomonZelman
x² - 100 = x² - 10² = (you tell me)
UsukiDoll
  • UsukiDoll
O_O ok what's the square root of 100?
SolomonZelman
  • SolomonZelman
u won't get a number, you should get `(blank)(blank)`
UsukiDoll
  • UsukiDoll
find the square root of 100 and the square root of x^2
SolomonZelman
  • SolomonZelman
Okay, maybe I should do a different example?
anonymous
  • anonymous
ok
UsukiDoll
  • UsukiDoll
maybe what's 10 x 10 !?!
anonymous
  • anonymous
100
UsukiDoll
  • UsukiDoll
all right.. so the square root of 100 is 10 so we've found one piece of the solution
UsukiDoll
  • UsukiDoll
\[(a^2-10^2)=(a+10)(a-10)\]
anonymous
  • anonymous
ok
UsukiDoll
  • UsukiDoll
so all we need to do is find the square root of x^2
anonymous
  • anonymous
what?
UsukiDoll
  • UsukiDoll
or if you memorize the formula let a = x
anonymous
  • anonymous
formula?
UsukiDoll
  • UsukiDoll
\[(a^2-10^2)=(a+10)(a-10)\] we had x^2 - 100 earlier and our formula is \[(a^2-b^2)=(a+b)(a-b) \]
UsukiDoll
  • UsukiDoll
so if b was 10 what's our a?
anonymous
  • anonymous
wait what
anonymous
  • anonymous
i'm confused
SolomonZelman
  • SolomonZelman
Problem: Factor: p²-49. Solution: We are going to apply the difference of squares formula that states: `a²-b²=(a+b)(a-b)` My a² in this case is p², and b² is 49. So, what will my a and b be? if a² is in this case p², then a is in this case p (you know why, right?) if my b² is 49, then my b is 7 (because √49 = 7) So, we end up getting: `p² - 49 = (p + 7)(p - 7)` (and this is the answer) `~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~` `~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~` Additional note. if you expand it beckwards you can see why this formula works. \(\Large\color{black}{ \displaystyle ({\rm \color{blue}{b}}+{\rm \color{red}{a}})({\rm \color{blue}{b}}-{\rm \color{red}{a}})= }\) \(\Large\color{black}{ \displaystyle {\rm \color{blue}{b}}({\rm \color{blue}{b}}-{\rm \color{red}{a}})+{\rm \color{red}{a}}({\rm \color{blue}{b}}-{\rm \color{red}{a}})=}\) \(\Large\color{black}{ \displaystyle {\rm \color{blue}{b}}^2-{\rm \color{red}{a}}{\rm \color{blue}{b}}+{\rm \color{red}{a}}{\rm \color{blue}{b}}-{\rm \color{red}{a}}^2=}\) \(\Large\color{black}{ \displaystyle {\rm \color{blue}{b}}^2~\cancel{-{\rm \color{red}{a}}{\rm \color{blue}{b}}}~\cancel{+{\rm \color{red}{a}}{\rm \color{blue}{b}}}-{\rm \color{red}{a}}^2=}\) \(\Large\color{black}{ \displaystyle {\rm \color{blue}{b}}^2-{\rm \color{red}{a}}^2.}\) So we therefore have: \(\Large\color{black}{ \displaystyle {\rm \color{blue}{b}}^2-{\rm \color{red}{a}}^2=}\)\(\Large\color{black}{ \displaystyle ({\rm \color{blue}{b}}+{\rm \color{red}{a}})({\rm \color{blue}{b}}-{\rm \color{red}{a}}) }\)
SolomonZelman
  • SolomonZelman
backwards*
UsukiDoll
  • UsukiDoll
your question is x^2-100 and in the form of \[(a^2-b^2)=(a+b)(a-b) \] so we've figured out that 10 x 10 = 100 and the square root of 100 is 10
anonymous
  • anonymous
ok
UsukiDoll
  • UsukiDoll
so from the formula if b = 10, then what should be our a hint: it's a variable and it's from x^2-100
UsukiDoll
  • UsukiDoll
\[x^2-100 \rightarrow (a^2-10^2)=(a+10)(a-10)\]
Nnesha
  • Nnesha
difference of square\[\huge\rm a^2- b^2 =(a+b)(a-b)\] so just take square root of FIRST TERM nd SQUARE ROOT of 2nd term \[\large\rm \sqrt{a^2}-\sqrt{b^2} =(a+b)(a-b)\] |dw:1437313113030:dw| one parentheses with plus sign and one with negative done!
anonymous
  • anonymous
i'm back
anonymous
  • anonymous
can someone just give me the answer
anonymous
  • anonymous
hello
Nnesha
  • Nnesha
ello
SolomonZelman
  • SolomonZelman
There is no use in giving you the answer, and thus I (and hope others as well) will not handle the answer this way. We have attempted a number of good explanation and none worked (some people even gave the answer away but not 100%). You are either not reading our replies, or there is a lack of knowledge to do this problem in the first place. I will suggest to review the post and your math textbook..... good luckl

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