Question

Can anybody explain how to solve this?

Answer 1

one way is multiply out each answer and see which one works.

Answer 2

concentrate on just the 1st term of the original expression
4 m^16

using FOIL you know that term comes from the First two terms of the factors

look at choice A: ( 2m^4 - 3 p^3)^2 = ( 2m^4 - 3 p^3) ( 2m^4 - 3 p^3)
the First terms, multiplied are 2*m^4 * 2 * m^4= 4 m^8
that does not match 4m^16 so A is out

Answer 3

if you do enough of these problems, you will notice (by its pattern) that you have a perfect square.

Answer 4

do as he suggested, expand A, B ,C, D you can get the answer easily, if you are lucky, you can get it quickly if the answer is A or B, right? save time on tests

Answer 5

Thank you!!! I think C would be the correct answer!!

Answer 6

if it 's c, the last term is (-3p^6)^2 = 9p^12 , it is not yours original one

Answer 7

I can't seem to get the answer:(

Answer 8

I think I am doing it wrong

Answer 9

what did you try ?

Answer 10

I tried the choices but I keep getting other answers

Answer 11

give an example of your work.

Answer 12

for all of the answers??!

Answer 13

I think B is the correct answer

Answer 14

show your work for B

Answer 15

ok, first I did (2m^8 -3p^6) (2m^8 +3p^6)

Answer 16

now do First, 2m^8 * 2m^8
what do you get ?

Answer 17

4m^16

Answer 18

now do O (for Outside or Outer)
the outsides are 2 m^8 and -3 p^6
what do you get ?

Answer 19

-2m^8 3p^3

Answer 20

6m^8 p^3

Answer 21

yes but remember 2*m^8*(-3)*p^3 can be written as 2*(-3)* m^8 p^3
2* -3 is -6
so you get
-6 m^8 p^3

Answer 22

now do Inner (the 2 terms on the "inside")
\[ -3 p^3 \cdot 2 m^8\]

Answer 23

I should correct choice B is

you mean
\[ (2m^8 -3p^3) (2m^8 -3p^3) \]

Answer 24

so B is the correct answer after all !

Answer 25

you should be able to work through it and show that B is correct.

Answer 26

4m^16 - 6m^8p^3 2m^8p^3 -9p^6

Answer 27

like this?

Answer 28

getting close. but the last two are not correct.

the 3rd term is
\[ −3p^3⋅2m^8 \]

that is short for multiplying out
\[ -3 \cdot p\cdot p\cdot p\cdot 2 \cdot m \cdot m\cdot m \cdot m\cdot m \cdot m\cdot m \cdot m\]
when you multiply you can switch the order, so you could write it as
\[ 2 \cdot-3 \cdot p\cdot p\cdot p\cdot m \cdot m\cdot m \cdot m\cdot m \cdot m\cdot m \cdot m\]
now 2 * -3 is -6 so this is
\[ -6\cdot p\cdot p\cdot p\cdot m \cdot m\cdot m \cdot m\cdot m \cdot m\cdot m \cdot m\]

but people use the short-cut and write p and a little 3 (it looks nicer) and m with 8
\[ -6 \cdot p^3 \cdot m^8 \]
also, people leave out the multiply sign (the dot), so the short form is
\[ -6 p^3 m^8 \]

Answer 29

what do you get for the last term
\[ -3 p^3 \cdot -3 p^3 \]

Answer 30

9p^6

Answer 31

so you get
\[ 4m^{16} - 6m^8p^3 -6 m^8p^3 +9p^6 \]

now the last step. if you have the same letters to the same power
(the m^8 p^3 in the two middle terms) you can combine them
you have -6 of m^8 p^3 and another -6 of the same thing...

combine to get -12 m^8 p^3
the final answer is
\[ 4m^{16} - 12m^8p^3 +9p^6 \]

Answer 32

if you practice, this gets easier (and faster)

Answer 33

Thanks a lot:( I hope it gets easier!!!:)

Answer 34

try this, if you have time
http://www.khanacademy.org/math/algebra/polynomials/multiplying_polynomials/v/multiplying-binomials

all the videos are good...