Question

Subtract and simplify: (2p2q – 3pq2 + q3) – (p2q + q3)

A. 2p2q – 3pq2

B. p2q – 3pq2

C. p2q – 2pq2

D. p2q – 3pq2+2q3

I thought this might be B but I wasn't sure...

Answer 1

@imqwerty @mathstudent55

Answer 2

@StudyGurl14

Answer 3

@tootzrll @Pinkybottom67

Answer 4

Someone....

Answer 5

Anyone.....

Answer 6

@Comrad

Answer 7

When you subtract a polynomial from another polynomial, you drop the parentheses of the first one.
Then to drop the parentheses of the second one, all signs inside the second parentheses change.

Answer 8

Okay

Answer 9

Here a simple example for you to see the change of signs.

\((a + 2b) - (2a - 3b)\)

\(=a + 2b - 2a + 3b\)

Answer 10

Oh that makes sense.

Answer 11

Notice carefully what was done from the first line tot eh second line above.

Answer 12

The first polynomial remained exactly as it was, only the parentheses are no longer there.
Notice (a + 2b) became a + 2b.

Answer 13

Right, you just drop them and nothing changes.

Answer 14

Now look at the second polynomial, the one being subtracted.
To do the part -(2a - 3b), we drop the parentheses by changing every sign inside the parentheses. In other words, think of the minus sign to the left of the parentheses as being -1, and you distribute the -1 inside the parentheses.

Answer 15

Inside the second parentheses, we had 2a - 3b.
The 2a became -2a (the sign changed from 2 to -2).
The -3b became + 3b ( the sign changed from -3 to +3).

Answer 16

Oh okay

Answer 17

Now that we have dealt with both sets of parentheses and have no parentheses left, we continue like we did for the sum of polynomials. We combine like terms.

Answer 18

Here is where we left off above:

\(=a + 2b - 2a + 3b\)

Now we move like terms together:

\(= a - 2a + 2b + 3b\)

Finally, we combine like terms:

\(= -a + 5b\)

Answer 19

Oh I see.

Answer 20

Now we can try your problem.

Remember again the steps.
Since the parentheses of the first polynomial are not necessary, we just drop the parentheses.
To drop the parentheses of the polynomial we are subtracting, we change every sign inside the second parentheses.
Then we combine like terms.

Answer 21

1. 2p^2 - 3pq^2 + q^3 - p^2q + q^3

Answer 22

Also, one more thing.
To be like terms, two terms must have exactly the same variables and exactly the same exponents on those variables.

Let's do your problem:

\((2p^2q - 3pq^2 + q^3) - (p^2q + q^3)\)

Answer 23

The first polynomial has parentheses which are not necessary. We simply drop them.

\(=2p^2q - 3pq^2 + q^3 - (p^2q + q^3)\)

Now we need to deal with the second parentheses.
To drop the second parentheses, after the minus sign, we must change every sign inside the second parentheses.

\(=2p^2q - 3pq^2 + q^3 - p^2q - q^3\)

Answer 24

Notice the last \(+ q^3\) becomes \(- q^3\).
Be careful with that.

Answer 25

A negative outside parentheses changes ALL signs inside the parentheses.
You see?

Answer 26

Oh yeah

Answer 27

We here here now:

\(=2p^2q - 3pq^2 + q^3 - p^2q - q^3\)

Now we move like terms together:

\(= 2p^2q - p^2q -3pq^2 + q^3 - q^3 \)

Ok so far?

Answer 28

Yep!

Answer 29

Now we combine like terms to finish our problem.

\(= p^2q -3pq^2 \)

Answer 30

You were correct again.
B is the answer.

Answer 31

Ok, sorry, but gtg.

Answer 32

Oh great!! Thanks again so much, You helped a lot :)

Answer 33

You're welcome.