Question

how to combine:

Answer 1

(x+2) (x-2)

Answer 2

difference of squares

Answer 3

multiply xs and the 2s

Answer 4

X x X then X x -2 then 2xX then 2 x -2

Answer 5

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

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

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

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

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

Answer 6

so, see how the middle term cancels?

Answer 7

And this is for any "a" and "b" values. The middle term always cancels.

Answer 8

making it \[x ^{2} -?\]

Answer 9

well, we just now proved that
\(\Large\color{black}{ \displaystyle ({\rm \color{blue}{b}}-{\rm \color{red}{a}})({\rm \color{blue}{b}}+{\rm \color{red}{a}})= {\rm \color{blue}{b}}^2-{\rm \color{red}{a}}^2}\)

Answer 10

right

Answer 11

\(\Large\color{black}{ \displaystyle ({\rm \color{blue}{x}}-{\rm \color{red}{2}})({\rm \color{blue}{x}}+{\rm \color{red}{2}})=??}\)

Answer 12

just compare the form

Answer 13

x^2 is right, and minus what ?

Answer 14

2

Answer 15

yes, so x^2-2^2

Answer 16

which is same as what? how can you simplify 2^2 ?

Answer 17

-4

Answer 18

yes, x^2-4

Answer 19

I can't really see the attachment. sorry

Answer 20

try zooming in plz

Answer 21

go to the view tab in that doc.

Answer 22

I think I see it

Answer 23

\(\large\color{black}{ \displaystyle \frac{3 }{8x^3y^3} -\frac{1 }{4xy} }\)


\(\large\color{gray}{ \displaystyle a.~~~~~\frac{x^2y^2-3}{4x^3y^3} }\)

\(\large\color{gray}{ \displaystyle b.~~~~~\frac{2x^2y^2-3}{8x^3y^3} }\)

\(\large\color{gray}{ \displaystyle c.~~~~~\frac{2}{8x^3y^3} }\)

\(\large\color{gray}{ \displaystyle d.~~~~~\frac{3-x^2y^2}{4x^3y^3} }\)

Answer 24

am I right ?

Answer 25

yes

Answer 26

okay, multiply top and bottom of the second fraction by BLANK.

this BLANK has to be making the denominator of the 2nd fraction [into] the same thing as the denominator of the 1st fraction \(\large\color{black}{ \displaystyle ( }\) i.e. [into] \(\large\color{black}{ \displaystyle 8x^3y^3 }\) in the denominator \(\large\color{black}{ \displaystyle ) }\).

Answer 27

right thats what i got

Answer 28

what did you get ?

Answer 29

\[\frac{ 3 }{ 8x ^{3} y ^{3}} - \frac{ 1 }{ 4xy }\]

Answer 30

oh, OPTION D, correction.

\(\large\color{red}{ \displaystyle \frac{3 -2x^2y^2}{8x^3y^3} }\)

Answer 31

how would you make the common denominator ?

Answer 32

\(\large\color{black}{ \displaystyle \frac{3 }{8x^3y^3} -\frac{1 \color{red}{\times 4x^2y^2}}{4xy\color{red}{\times 4x^2y^2}} }\)

am I correct, or am I making a little mistake ?

Answer 33

Your right!

Answer 34

no I am not... are you sure?

Answer 35

with this multiplication, do I get the common denominator ?

Answer 36

why are you timing 4*4

Answer 37

to get you to correct me, lol

Answer 38

8-8 =0

Answer 39

so, what should I multiply on top and bottom of the 2nd fraction then ?

Answer 40

im thinking 1 so that way 1*4=4 then 8=4 equals 4... but then that wouldnt be right considering we need 8 so probbaly 4*1

Answer 41

or is that wrong?

Answer 42

Im going with 1

Answer 43

\(\large\color{black}{ \displaystyle \frac{3 }{8x^3y^3} -\frac{1 \color{red}{\times \color{blue}{2}x^2y^2}}{4xy\color{red}{\times \color{blue}{2}x^2y^2}} }\)

Answer 44

that would make it a common denominator, wouldn't it ?

Answer 45

can you finish simplifying this fraction?

Answer 46

im trying

Answer 47

so im going with D considering i got 3in the numerator and 8 in the denomenator

Answer 48

actually if iwent 3-2 that would be 1 so it could be A

Answer 49

yeah so on top of that i'd also get 4 in the bottom so its A for sure

Answer 50

@pitamar