## anonymous one year ago Factor: x2 - 100

1. Vocaloid

hint: (A^2-B^2) = (A+B)(A-B) x^2 - 100 = ?

2. SolomonZelman

yes, and 100=10² as you probably know already.

3. UsukiDoll

difference of squares formula $(a^2-b^2)=(a+b)(a-b)$

4. anonymous

is it 1000? IDK

5. SolomonZelman

x² - 100 = x² - 10² = (you tell me)

6. UsukiDoll

O_O ok what's the square root of 100?

7. SolomonZelman

u won't get a number, you should get (blank)(blank)

8. UsukiDoll

find the square root of 100 and the square root of x^2

9. SolomonZelman

Okay, maybe I should do a different example?

10. anonymous

ok

11. UsukiDoll

maybe what's 10 x 10 !?!

12. anonymous

100

13. UsukiDoll

all right.. so the square root of 100 is 10 so we've found one piece of the solution

14. UsukiDoll

$(a^2-10^2)=(a+10)(a-10)$

15. anonymous

ok

16. UsukiDoll

so all we need to do is find the square root of x^2

17. anonymous

what?

18. UsukiDoll

or if you memorize the formula let a = x

19. anonymous

formula?

20. UsukiDoll

$(a^2-10^2)=(a+10)(a-10)$ we had x^2 - 100 earlier and our formula is $(a^2-b^2)=(a+b)(a-b)$

21. UsukiDoll

so if b was 10 what's our a?

22. anonymous

wait what

23. anonymous

i'm confused

24. 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: $$\Large\color{black}{ \displaystyle {\rm \color{blue}{b}}^2-{\rm \color{red}{a}}^2=}$$$$\Large\color{black}{ \displaystyle ({\rm \color{blue}{b}}+{\rm \color{red}{a}})({\rm \color{blue}{b}}-{\rm \color{red}{a}}) }$$

25. SolomonZelman

backwards*

26. 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

27. anonymous

ok

28. 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

29. UsukiDoll

$x^2-100 \rightarrow (a^2-10^2)=(a+10)(a-10)$

30. 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!

31. anonymous

i'm back

32. anonymous

can someone just give me the answer

33. anonymous

hello

34. Nnesha

ello

35. 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