Question

please see attached.
my question is how do i form the exponents

Answer 1

Example: 2x2x2x2 would be 2^4

Answer 2

did you look at the attachment???

Answer 3

for the 1st example

notice that the first line, all the terms have exponents that add up to 4
each term is alphabetical ab
they start with the highest exponent (4) for a and the lowest for b (0)
a^4 b^0 is just a^4 * 1 or just a^4
then you go down 1 on the a exponent and up 1 on the b exponent.

Answer 4

In the first line, the exponents of the ab terms add to 4
in the 2nd line the exponents of the ab terms add to 3
the answer line, the exponents add to 4+3 = 7
so the answer is in the order
a^7 b^0 a^6 b^1 a^5 b^2 .... a^1 b^6 a^0 b^7

Answer 5

but there is no a^6

Answer 6

notice that you multiply all these ab terms by the coefficients of the calculation
the coeff for a^6 b^1 is 0, so we don't bother to write it down

Answer 7

sorry i am completely lost

Answer 8

what do you mean when you said the "the first all the terms have exponent that add up to 4"????

Answer 9

I meant in the first equation:
a^4 - 3a^2b^2 ....
notice that a^4 is the same as a^4 b^0 (right?) and 4+0=4
in -3a^2 b^2 we again have 2+2=4
and so on for each term...

Answer 10

ok

Answer 11

is the coefficient for a^6 b^1 zero because it is not in either of the original equations???

Answer 12

It looks like it. But notice they got a zero for a^4b^3 which happened because things canceled.

to use this technique they started with
\[ a^4 -3a^2b^2 +2ab^3+b^4\]
they then make a grid with the exponents for a and b
4,0 3,1 2,2 1,3 0,4 (I'm abbreviating here. those are the exponents)
then they fill in the coefficients in the correct column

4,0 3,1 2,2 1,3 0,4
1 -3 2 1

if any are missing, put in a zero
4,0 3,1 2,2 1,3 0,4
1 0 -3 2 1

Answer 13

they did the same thing for the other polynomial to get
1 0 -2 -2

then they put one set of coefficients below the other, lining up on the left side
(this is different from when we do 312 x 21 where we line them up on the right side)

1 0 -3 2 1
1 0 -2 -2

then they multiply going left to right
the first 1 in the bottom times every number in the top row gives you
1 0 -3 2 1

then mult by 0 and go in one place to the right:
1 0 -3 2 1
0 0 0 0

then -2 times the top row. put the answer starting below the -2

1 0 -3 2 1
0 0 0 0
-2 0 6 -4 -2

then the last -2 times the top row
1 0 -3 2 1
0 0 0 0
-2 0 6 -4 -2
-2 0 6 -4 -2

then add up the columns
1 0 -5 0 7 2 -6 -2

now assign ab with the correct exponents

Answer 14

7,0 6,1 5,2 4,3 3,4 2,5 1,6 7
1 0 -5 0 7 2 -6 -2

Answer 15

\[ a^7 -5a^5b^2 +7a^3b^4 +2a^2b^5 -6ab^6 -2b^7 \]

Answer 16

thanks phi