Question

Factor: x2 - 100

Answer 1

hint:

(A^2-B^2) = (A+B)(A-B)

x^2 - 100 = ?

Answer 2

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

Answer 3

difference of squares formula
\[(a^2-b^2)=(a+b)(a-b) \]

Answer 4

is it 1000?
IDK

Answer 5

x² - 100 = x² - 10² = (you tell me)

Answer 6

O_O
ok what's the square root of 100?

Answer 7

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

Answer 8

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

Answer 9

Okay, maybe I should do a different example?

Answer 10

ok

Answer 11

maybe what's 10 x 10 !?!

Answer 12

100

Answer 13

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

Answer 14

\[(a^2-10^2)=(a+10)(a-10)\]

Answer 15

ok

Answer 16

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

Answer 17

what?

Answer 18

or if you memorize the formula let a = x

Answer 19

formula?

Answer 20

\[(a^2-10^2)=(a+10)(a-10)\]

we had x^2 - 100 earlier and our formula is \[(a^2-b^2)=(a+b)(a-b) \]

Answer 21

so if b was 10 what's our a?

Answer 22

wait what

Answer 23

i'm confused

Answer 24

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:

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

Answer 25

backwards*

Answer 26

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

Answer 27

ok

Answer 28

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

Answer 29

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

Answer 30

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
\[\large\rm \sqrt{a^2}-\sqrt{b^2} =(a+b)(a-b)\]

one parentheses with plus sign and one with negative done!