Question

Find the complete factored form of the polynomial

Answer 1

\[a ^{8}b ^{4}+a ^{2}b ^{2}\]

Answer 2

What are your thoughts on this?

Answer 3

uhhhh confusing

Answer 4

So \(a^8\) is 8 \(a\) multiplied together right

Answer 5

What's common among the terms \(a^8b^4\) and \(a^2b^2\)?

Answer 6

no its something to do with the greatest common factor

Answer 7

I thought this topic is factorization?

Answer 8

idk im confused thats why i posted it

Answer 9

I know you're confused that's why I'm guiding you

Answer 10

Let's rewrite \(a^8b^6\) as \(a\times a\times a\times a\times a\times a\times a\times a\times b\times b\times b\times b\times b\times b\)

Answer 11

And rewrite \(a^2b^2\) as \(a\times a\times b\times b\)

Answer 12

So now what's common between them?

Answer 13

@megangray32 got any thoughs on this? alright i get that part

Answer 14

Okay so you don't trust me

Answer 15

not what i ment ok i need a couple opinions

Answer 16

okay sorry

Answer 17

its fine

Answer 18

What's common between \(a\times a\times a\times a\times a\times a\times a\times a\times b\times b\times b\times b\times b\times b\) and \(a\times a\times b\times b\)?

Answer 19

idk?

Answer 20

Or should I put it this way

Answer 21

How many \(a\)'s are common among them?

Answer 22

8?

Answer 23

Does \(a\times a\times b\times b\) have 8 \(a\)'s?

Answer 24

umm no

Answer 25

the question is
a^8b^4 + a^2b^2

why don't you convert it in the form
\[(x ^{n})^{m} + (y ^{o})^{m}\]

Answer 26

is supposed to look something like number(numbers)

Answer 27

Or let's do it this way

Answer 28

I'll show you the steps

Answer 29

sorry! I didn't get you..! @ilovebmth1234

Answer 30

And you'll tell me which step you don't understand

Answer 31

Okay?

Answer 32

terribly confused guys v.v

Answer 33

\[a^8b^4+a^2b^2\]\[=a^{2+6}b^{2+2}+a^2b^2\]\[=a^2a^6b^2b^2+a^2b^2\]\[=a^2(a^6b^2b^2+b^2)\]\[=a^2b^2(a^6b^2+1)\]

Answer 34

Tell me which step you don't understand

Answer 35

And don't be freaked out by the intensity, or we can't help you

Answer 36

oh my

Answer 37

So you're freaked out by the intensity

Answer 38

Which means that we cannot actually help you

Answer 39

So which step did you not understand

Answer 40

i just do not get the whole subject

Answer 41

Oh...

Answer 42

So shall we start by indices

Answer 43

sure

Answer 44

Do you remember the Laws of Indices?

Answer 45

no what grade you in?

Answer 46

9th grade, but that doesn't matter

Answer 47

Have you encountered something like \(a^{m+n}=a^ma^n\)?

Answer 48

so am i i havent learned that yet though for some reason

Answer 49

okay...

Answer 50

So...

Answer 51

Try to find \(a^2\times a^3\)

Answer 52

Hint: expand the whole expression

Answer 53

yeah

Answer 54

Find \(a^2\times a^3\)

Answer 55

a^4

Answer 56

Okay I know what I should do

Answer 57

what?

Answer 58

Here's an example:
\[a^3\times a^4=(a\times a\times a)(a\times a\times a\times a)=a\times a\times a\times a\times a\times a\times a=a^7\]

Answer 59

Now do the same thing to \(a^2a^3\)

Answer 60

a*a*a*a*a=a^4