Question

Write the expression -3x 2 + 2y 2 + 5xy - 2y + 5x 2 - 3y 2 in simplest form. Then, answer the following questions using complete sentences.

Answer 1

do you see any "like terms" that you can combine ?

Answer 2

no I dont understand it

Answer 3

your equation is this (btw, you should use ^ to show exponents)
-3x ^2 + 2y ^2 + 5xy - 2y + 5x^ 2 - 3y^ 2
if we use the equation editor (see button on the lower left)
\[ -3x ^2 + 2y ^2 + 5xy - 2y + 5x^ 2 - 3y^ 2 \]

a "like term" is the same variable (letter) to the same exponent. the number in front does not matter.
do you see any "like terms" ?

Answer 4

_3x^2 and 5x^2

Answer 5

yes, but that is a minus sign in front of the 3
\[ -3x^2 + 5x^2 \]
now we use this idea: you have 5 "x squared"s and take away 3 "x squared"s
how many \(x^2\) do you have left ?

Answer 6

idk

Answer 7

how about if you had 5 brooms and took away 3 brooms. How many brooms do you have?

or you have 5 apples and take away 3 apples ?
or 5 x^2 take away 3 x^2, how many x^2 ?

Answer 8

2

Answer 9

yes. so
\[ -3x^2 + 5x^2 = 2 x^2\]
you start with 5 of the x-squareds and take away 3 of them. that leaves you with 2 of them

Answer 10

so thats the answer

Answer 11

that is part of the answer. so far, we started with
\[ {-3x ^2} + 2y ^2 + 5xy - 2y + 5x^ 2 - 3y^ 2 \]
you simplified the x^2 part (combined them) so you now have
\[ 2x ^2 + 2y ^2 + 5xy - 2y - 3y^ 2 \]

can you find any more "like terms" ? hint: there are more

Answer 12

2x^2and 2y^2

Answer 13

a "like term" is the same variable (letter) to the same exponent. the number in front does not matter.

Answer 14

ok

Answer 15

2x^2and 2y^2 have DIFFERENT letters, so NOT like terms. keep looking

Answer 16

2y2 and 3y2

Answer 17

we have to be careful about the signs. One way to write this is
\[ 2x ^2 + {\bf2y ^2} + 5xy - 2y + {\bf- 3y^ 2} \]

so the two like terms are
\[ 2y^2 \text{ and } -3y^2 \]

Answer 18

can you combine them ? (you get a negative number out front)

Answer 19

what you mean combine them

Answer 20

\[ 2y^2 - 3y^2 \]
means you have 2 y-squared and take away 3 y-squared

Answer 21

do you know how to do
2 - 3 ?

Answer 22

yea

Answer 23

what do you get ?

Answer 24

-1

Answer 25

and that is the clue to what is
\[ 2y^2 - 3 y^2 \]

Answer 26

ok

Answer 27

what do you get ?

Answer 28

2 y-squared and take away 3 y-squared leaves how many y^2 ?

Answer 29

1

Answer 30

almost. \[ 2y^2 - 3y^2 \text{ is not } 1y^2 \]

\[ 3 y^2 - 2 y^2 = 1y^2 \]

Answer 31

-1y^2

Answer 32

you get a *negative number* of y^2

Answer 33

yes. now we have
\[ 2x ^2 + {\bf2y ^2} + 5xy - 2y + {\bf- 3y^ 2} \]
simplifies (by combining the y^2 terms) to
\[ 2x ^2 + {\bf-y ^2} + 5xy - 2y \]
or
\[ 2x ^2-y ^2+ 5xy - 2y \]

Answer 34

notice that -1y^2 is usually written as -y^2
(it means the same thing)

Answer 35

i understand it now the answer is 2x^2-y^2=5xy-2y i think is it right?

Answer 36

there is no = sign, unless there was an = sign in the original

Answer 37

ok

Answer 38

I guess you made a typo, and meant +

Answer 39

can you do the rest of the problem
Then, answer the following questions using complete sentences.

Answer 40

what to do now