Question

Simplify the expressions below. Write the final product in standard form and show your work. The pictures are in the comments.
1. 2x^4(4x^2 + 3x + 1)
2. (4x – 3)(2x^2 – 7x + 1)
3. (x^2 + 4x – 3)(2x^2 + x + 6)
4. Write a simplified polynomial expression to represent the area of the rectangle below.
5. Write a simplified polynomial expression to represent the area of the square tile, shown below.

Answer 1

The pictures are for 4 and 5

Answer 2

the top is for number 4 the bottom is for number 5

Answer 3

please help!

Answer 4

Since I can't get my work done, I'll try a little bit of yours. :)
This is a great site. http://www.wolframalpha.com/input/?i=simplify++2x%5E4%284x%5E2+%2B+3x+%2B+1%29+

ok. now I'll look at it more.

Answer 5

i have tried that site before it isn't always accurate and thank you so much! i owe you one!

Answer 6

1. 2x^4(4x^2 + 3x + 1)

multiply the \[2x ^{4}\] through to the others. \[(2x ^{4}*4x ^{2})+(2x^{4}*3x)+(2x^{4}*1) \]
\[=8x^{6}+6x^{5}+2x^{4}\]

Ok. I multiplied #1 myself. The site was right for that one. :)

Answer 7

exponents next to each other, like x^2*x^3 they add. to give x^5. exponents multiply if they are to the power of each other, like (x^2)^3, gives x^6.

Answer 8

(4x – 3)(2x^2 – 7x + 1)
\[4x*2x^{2} - 4x*7x +4x*1 -3*2x^{2} +3*7x -3*1\] Note the +3*7x, since the negative*negative=positive.
Multiply out the terms:
\[8x^{3}-28x^{2}+4x-6x^{2}+21x-3\] wow, this is more difficult on the computer than by hand. :)
Combine like terms (simplify):
\[8x^{3}-34x^{2}+25x-3\]
My computer is so slow :(
Double check that my sol is "standard form"...

Answer 9

it is :)

Answer 10

The same is done for #3. do you still need help w that one too?

Answer 11

yes my brain is fried if it isnt any trouble

Answer 12

OK. Mine too. that is why i'm avoiding my Q's
ok. give a sec

Answer 13

(x^2 + 4x – 3)(2x^2 + x + 6)
Let's take the first () multiplied through the second () :
x^2*(2x^2 + x + 6) + 4x*(2x^2 + x + 6) - 3*(2x^2 + x + 6)

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

\[(2x^4 + x^3 + 6x^2) + (8x^3 + 4x^2 + 24x) - (6x^2 + 3x + 18) \]
remove the (), but take into account that minus, so it is like multiplying (-1) through the whole last () set.
\[2x^4 + x^3 + 6x^2 +8x^3 + 4x^2 + 24x - 6x^2 - 3x - 18 \]
combine like terms:
\[2x^4 + 9x^3 + 4x^2 + 21x - 18 \]
and it matches that site, yay or me. :) typing really is more difficult. :)

Answer 14

*yay for me... typo

Answer 15

thank you i can do the rest!

Answer 16

ok! good luck!

Answer 17

if you ever need anyhting just message me!

Answer 18

can you help with one more question?

Answer 19

I need college probability and linear algebra :) I posted a Q but no one has gotten to it yet. No worries though.

Answer 20

http://openstudy.com/study#/updates/4f68c3aae4b0f81dfbb5a006

Answer 21

oh let me see if i can help, not good at the stuff though lol

Answer 22

You have two matrices of the same size. Compare rank(A+B) and rank(A)+rank(B) and prove.

Answer 23

ahhh nope can't do that lol

Answer 24

thought you meant something different

Answer 25

no worries. i didnt take the class, that is why i don't know how to do it. :)

ok, let me read your other link

Answer 26

Find the two products below. Compare and contrast, in complete sentences, the similarities and differences of the two.
(x + 6)(x - 6) and (x - 6)(x - 6)

Ok, the hoblos reply is right.
\[(x+6)(x-6) = x^2 -6x +6x -36\]
which simplifies by the -6x and +6x cancelling.
\[x^2-36\]
Yes, this is difference of two squares, http://en.wikipedia.org/wiki/Difference_of_two_squares


I suppose you could compare that they both give the x^2 and the 36, but due to the sign differences the 36 is positive for the one below and negative for the one above. Also, due to the sign difference in the one above, the -6x cancels the +6x.
I'm not sure what else to add. I'll have to think a bit.

\[(x - 6)(x - 6) = (x-6)^2 = x^2 -6x-6x +36=x^2 -12x +36\]

Answer 27

OKAY THANK YOU!

Answer 28

oops caps locks

Answer 29

welcome!