Question

best answer receives a medal and fan ;);):):):):):):)



an expression is shown below:
2x^3y+18xy-10x^2y-90y
part a.) rewrite the expression so that the the GCF is factored completely.
part b.) rewrite the expression completely factored. show all steps
part c.) if the two middle terms were switched so the expression became 2x^3y-10x^2+18xy-90y would the factored expression no longer be equivalent to your answer in part b? explain in detail

Answer 1

the GCF (greatest common factor) is the number (and letters) that you can factor out of each term.

there are two parts.
First, the letters: are there any letters that are in each and every term ?

Answer 2

x and y

Answer 3

A term is separated by a + or a -

I see a y in each term. What about the last term? Does it have an x ?

Answer 4

ooo sorry I didn't see the last term only had a y

Answer 5

ok, so you know you can factor out a "y" from each term
now for the numbers. One way is look at the term with the smallest number

that is 2x^3y, and 2 is the number. Does 2 divide evenly into each number in all of the terms ?

Answer 6

nope

Answer 7

which number does 2 not divide into ?

Answer 8

3

Answer 9

oh.. the 3 is a exponent.
the expression looks like this
\[ 2x^3y+18xy-10x^2y-90y \]
people make it little and put in the upper right so that you don't mix it up with the "big" numbers' out front.

the x^3 is short hand for x*x*x (3 x's multiplied together)

for factoring out the numbers, only the big numbers count.

Answer 10

oooo

Answer 11

you should see that each of the numbers out front can be evenly divided by 2
also each term can be divided by y

2y is the GCF that you can factor out.

can you factor 2y out of each term ? what do you get ?