Question

@jim_thompson5910 I multiply the stuff in the first parenthesis by the stuff in the second parenthesis, right? http://www.sketchtoy.com/34803580

Answer 1

9 multiplies, then add "like terms"

Answer 2

9?!

Answer 3

yes. 9!

what do you get for the first 3 : x^2 times each of the terms on the right side ?

Answer 4

Ohh, wait, I see why.

Answer 5

http://www.sketchtoy.com/34804492 Do I multiply 4x by the red equation next?

Answer 6

how did you get the red equation?

the way to do it is start with x^2, and multiply x^2 times
2x^2
x
+6

and write down the answer for each of those

then multiply 4x times each of
2x^2
x
+6

then multiply -3 times each of
2x^2
x
+6

Answer 7

do you know how to do
\[ x^2 \cdot 2x^2 \]?
remember this is the same as
\[ x\cdot x \cdot 2 \cdot x \cdot x \]
and you can change the order of the multiplies to
\[ 2 \cdot x\cdot x \cdot x \cdot x \]
and use the "short-hand" x^4 instead of x*x*x*x
\[ 2 x^4 \]

Answer 8

Give me some background information on what you're doing. It appears we're dealing with multiplication of trinomials.

Answer 9

The worksheet is actually called Multiplication of Polynomials.

Answer 10

Poly, whateva. Okay, so in order to multiply a trinomial we want to multiply every time by on another.

Answer 11

I have this down so far http://www.sketchtoy.com/34804492

Answer 12

http://www.sketchtoy.com/34806815

Answer 13

Then you just have to add like terms

Answer 14

So the red equation I have down already.. would I multiply that by 4x now?

Answer 15

Huh, the 4x in the original equation? You want to multiple every term...

Answer 16

No, the red equation in this: http://www.sketchtoy.com/34804492 is the product of multiplying x^2 by the original equation.

Answer 17

http://www.sketchtoy.com/34808129

Answer 18

Then you multiply by -3

Answer 19

Whoa, where did that second part come from?

Answer 20

I multiplied 4x by everyting in the second equation.

Answer 21

Oh, okay! So then I multiply both the red and blue by -3?

Answer 22

No. You multiply everything by -3 on the 2nd parenthesis.

Answer 23

Are you aware of what we're even doing? :/

Answer 24

Yes, I'm just really really bad at it > . <

Answer 25

Right there? http://www.sketchtoy.com/34809182

Answer 26

If I had

(x + y + z) (x + y + z)

I'd multiply everything by x

x^2 + xy + xz

Then I'd do the same for every other term

yx + y^2 + yz

And now time for z

zx zy z^2

Does that make sense?

Answer 27

yes, i'll just wing it i guess.

Answer 28

http://www.sketchtoy.com/34809503

Answer 29

and now add all the like terms?

Answer 30

This is actually really easy I just think you're making it more difficult than it actually is.. http://www.sketchtoy.com/34809753

I second, I'll draw something up for you

Answer 31

This is too confusing. I'm just going to ask my teacher. Thanks for the help though.

Answer 32

No no. I'm already drawing something. yOu will wait!

Answer 33

The first term in that initial multiplication is wrong: x^2 * 2x^2 is not 3x^4!

Answer 34

See what I did here? http://www.sketchtoy.com/34810550

This is literally one of the easiest things you can do in school :/

Answer 35

Here's the way to think about it:

Remember the distributive property of multiplication?
\[a(b+c) = ab + ac\]
We just apply that several times:
\[a(b+c+d) = ab + ac + ad\]
\[(a+b+c)(d +e + f) = a(d+e+f) + b(d+e+f) + c(d+e+f) \]\[= ad + ae + af + b(d + e + f) + c(d + e + f)\]\[= ad+ae+af + bd + be + bf + c(d + e + f)\]\[= ad + ae + af + bd + be + bf + cd + ce +cf\]

Answer 36

So your problem:
\[(x^2+4x-3)(2x^2+x+6) = x^2(2x^2+x+6) + 4x(2x^2+x+6) -3(2x^2+x+6)\]\[=2x^4+x^3+6x^2 + 8x^3+4x^2+24x -6x^2-3x-18\]
Collect like terms and you're done!

Answer 37

Sorry if part of it went off the right side, I hope you get the idea...

Answer 38

@Compassionate That's what I've been doing, I was only one number off. And you know that very last number is a 6, right?

Answer 39

I thought it was b. Your handwriting is scary ;-;

Yea, do what you did for the first one to every term in the first set of parentheses.

Answer 40

Sorry, homeschooling does horrible things to handwriting. > . <
And okay.

Answer 41

http://www.sketchtoy.com/34812439 This is the first round, right?

Answer 42

You messed up on the last part. http://www.sketchtoy.com/34812644

Answer 43

Round 2 is in purple: http://www.sketchtoy.com/34813148

Answer 44

correct. Now the same for -3

Answer 45

http://www.sketchtoy.com/34813715 Round 3 in dark blue

Answer 46

Last term in the red should be \(6x^2\) not \(6^2\)

Answer 47

Oops, thanks for catching that @whpalmer4

Answer 48

http://www.sketchtoy.com/34813953

Answer 49

Now add like terms

Answer 50

I don't know how I would add the last three terms because they aren't like :/

Answer 51

For simplicity lets add the first two: http://www.sketchtoy.com/34815249

Answer 52

is it 12x^2

Answer 53

http://www.sketchtoy.com/34815434

Answer 54

warning, you lost the last part of the sum in that sketch...

Answer 55

I fixed it.

Answer 56

You're too quick for me :-)

Answer 57

She just gave up. Ha ha :P