OpenStudy (anonymous):

3a^2(a-2)(a^2+2a+4)

6 years ago
OpenStudy (saifoo.khan):

3 a^5-24 a^2

6 years ago
OpenStudy (anonymous):

oh yea, and a=-7

6 years ago
OpenStudy (anonymous):

\[3a^2 * (a-2) * (a^2 + 2a + 4)\]

6 years ago
OpenStudy (saifoo.khan):

a = -7

6 years ago
OpenStudy (saifoo.khan):

??

6 years ago
OpenStudy (anonymous):

it says solve the equation if a=-7

6 years ago
OpenStudy (anonymous):

here you use various properties of multiplication

6 years ago
OpenStudy (anonymous):

yay! i love to multiply!! (well my calculator does) :P

6 years ago
OpenStudy (anonymous):

Start with \[3a^2*(a-2)\]

6 years ago
OpenStudy (saifoo.khan):

just write -7 instead of a.

6 years ago
OpenStudy (anonymous):

Here you will use the distributive property

6 years ago
OpenStudy (anonymous):

\[3a^2 *(a-2)\] = \[3a^2 * a - 2 *3a^2\]

6 years ago
OpenStudy (anonymous):

okay.

6 years ago
OpenStudy (anonymous):

You don't need a calculator here

6 years ago
OpenStudy (anonymous):

i understand so far.

6 years ago
OpenStudy (anonymous):

So, what does this become? \[3a^2 * a - 2 *3a^2\]

6 years ago
OpenStudy (anonymous):

simplify it

6 years ago
OpenStudy (anonymous):

okay. so 9a^4 times a -2

6 years ago
OpenStudy (anonymous):

How did you get that?

6 years ago
OpenStudy (anonymous):

3 a squared times 3 a squared. i think...

6 years ago
OpenStudy (anonymous):

You have \[3a^2 *a - 2*3a^2\]

6 years ago
OpenStudy (anonymous):

right.

6 years ago
OpenStudy (anonymous):

On the first term, \[3a^2*a\] you just do some multiplying and get \[3a^2*a=3a^3\] because \[3a^2=3*(a^2)=3*(a*a)\] and you are just mulitplying by another \[a\]

6 years ago
OpenStudy (anonymous):

right. so its 3a^3-2*3a?^2

6 years ago
OpenStudy (anonymous):

second term, ignore the negative for now: \[2*3a^2\] just more good ol' multiplying of \[2*3\]

6 years ago
OpenStudy (anonymous):

so 6a^2?

6 years ago
OpenStudy (anonymous):

so finally, you get \[(3a^3 - 6a^2)\]

6 years ago
OpenStudy (anonymous):

Yes

6 years ago
OpenStudy (anonymous):

You can't do anything else really to these terms, the have a raised to different values

6 years ago
OpenStudy (anonymous):

\[(3a^3 - 6a^2)*(a^2+2a+4)\]

6 years ago
OpenStudy (anonymous):

That is what is left of the original relation

6 years ago
OpenStudy (anonymous):

i understand now! okay, thank you dpflan.

6 years ago
OpenStudy (anonymous):

Now you can use the distributive property again

6 years ago
OpenStudy (anonymous):

If you want to check your answer, I'll be around

6 years ago
OpenStudy (anonymous):

okay, awesome! (:

6 years ago
OpenStudy (anonymous):

OK, what'd you get?

6 years ago
OpenStudy (anonymous):

3a^5-24a^2

6 years ago
OpenStudy (anonymous):

\[(3a^3 - 6a^2)*(a^2+2a+4)\]

6 years ago
OpenStudy (anonymous):

First distribute \[3a^3\] by multiplying \[(3a^3)*(a^2 + 2a +4)\]

6 years ago
OpenStudy (anonymous):

that would be....

6 years ago
OpenStudy (anonymous):

3a^5+12a^3-12a^3-24a^2

6 years ago
OpenStudy (anonymous):

\[a^m * a^n = a^{n+m}\]

6 years ago
OpenStudy (anonymous):

There should only be 3 terms for this part

6 years ago
OpenStudy (anonymous):

\[(3a^3)*(a^2) + (3a^3)*2a + (3a^3)*4\]

6 years ago
OpenStudy (anonymous):

3a^5+6a^2+12a^3

6 years ago
OpenStudy (anonymous):

yep, missing the ^4 on the second, but you got it

6 years ago
OpenStudy (anonymous):

yay!

6 years ago
OpenStudy (anonymous):

now for the 2nd part: \[(6a^2)*(a^2 + 2a + 4)\]

6 years ago
OpenStudy (anonymous):

We can ignore the \[-\] for now

6 years ago
OpenStudy (anonymous):

6a^4+12a^3+24a^2

6 years ago
OpenStudy (anonymous):

We just need to remember it at the end, or we can keep if that's less confusing

6 years ago
OpenStudy (anonymous):

(-6a^2)*(a^2 + 2a + 4)

6 years ago
OpenStudy (anonymous):

\[(-6a^2)*(a^2 + 2a + 4)\]

6 years ago
OpenStudy (anonymous):

-6a^4-12a^3-24a^2

6 years ago
OpenStudy (anonymous):

yeah, cool

6 years ago
OpenStudy (anonymous):

Now combine the results of part 1 and part 2, make sure to group like terms, like the a^2's with the a^2's

6 years ago
OpenStudy (anonymous):

\[(3a^5+6a^4+12a^3) + (-6a^4-12a^3-24a^2) \]

6 years ago
OpenStudy (anonymous):

\[3a^5 + (6a^4 - 6a^4) + (12a^3 - 12a^2) - 24a^2\]

6 years ago
OpenStudy (anonymous):

3a^5+12a^3-12a^3-24a^2

6 years ago
OpenStudy (anonymous):

One more subtraction ;)

6 years ago
OpenStudy (anonymous):

3a^5-24a^2

6 years ago
OpenStudy (anonymous):

Bam!

6 years ago
OpenStudy (anonymous):

woo-hoo!!!!! (: so happy right now!!!!! thank you sooooo much dpflan, or daniel !!!!!! (: i can't thank u enough for your help!

6 years ago
OpenStudy (anonymous):

Hey, no problem, you could do, just remember to go step by step

6 years ago
OpenStudy (anonymous):

i will definitely do that! gotta go now, my mom's turning off the computer, so i am about to lose the wifi! thanks again!

6 years ago
OpenStudy (anonymous):

No problem, I think you got it

6 years ago
OpenStudy (anonymous):

i think i do to....too....to. :)

6 years ago
OpenStudy (anonymous):

too!

6 years ago