Question

Simplify the expressions. Show your work.

Answer 1

@Nnesha

Answer 2

@phi ???

Answer 3

- in front of the parens means - each term inside
or, think of -( a+b+c) as
-1* (a+b+c)
and you "distribute" the -1 to get -1*a + -1*b+-1*c
or
-a + -b + -c

so the first step is distribute the -1 in front of the second set of parens
can you do that ?

Answer 4

I think I know what you mean but could you help me do it?

Answer 5

@phi

Answer 6

I can give you an example
\[ -(x^4 +2x^3) = -1 \cdot (x^4 +2x^3)\\ =-1\cdot x^4 + -1\cdot 2x^3\\
= -x^4 + -2x^3
\]
do you see the "rule"?
can you try doing that for
\[ -(3x^3 + 11x^2 -8x)\]
what do you get ?

Answer 7

what is -1 * 3x^3 ?

Answer 8

-3X^3 ?

Answer 9

@phi

Answer 10

yes. that is the first term you get when you distribute the -1 in
\[ -(3x^3 + 11x^2 -8x) \]
now do the next term (the 11x^2) . what do you get ?

Answer 11

-11X^2 ?

Answer 12

yes
now the last term. if it helps, remember that
\[ -(3x^3 + 11x^2 -8x) = -(3x^3 + 11x^2 + -8x) \]
(in other words, think of the last term as -8x)
-1 * -8x is ?

Answer 13

Would it -8x

Answer 14

in algebra we (lots of times) leave out the multiply sign
by
-1*-8x means -1* -8 * x
what is -1* -8 ?

Answer 15

minus times a minus is a plus (always a puzzle, but that is how the world works)

Answer 16

would it become just 8x no negative?

Answer 17

yes
-1*-8*x
do the first multiplies: -1*-8 is +8
so the simplified version is
8*x
or (in algebra)
8x
(which means 8 times x)

Answer 18

okay! Cool.

Answer 19

so now you have changed the last part of the problem to
\[ -3x^3 -11x^2 +8x \]
and the problem is now
\[ 5x^4 -3x^3 +6x -3x^3 -11x^2 +8x \]

now look for "like terms"
that means look for the same variable with the *same exponent*
there is only one term with x^4
so write that term down as the first part of the answer.

Answer 20

now look for x^3 terms. I assume you see them?

Answer 21

so write down 5x^4 ?

Answer 22

yes

Answer 23

now look for x^3 terms.

Answer 24

so now write down -3x^3 ?@phi

Answer 25

except there are two "terms"
-3x^3 and *another* -3x^3 term in
\[ 5x^4 -3x^3 +6x -3x^3 -11x^2 +8x \]
do you see them ?

Answer 26

yes I do now. They are the same. so write those down seperatly, next to the 5x^4 ?

Answer 27

we could write them separately, but when they are "like terms" we can simplify
think: I have -3 of x^3 and another -3 of x^3
or -3x^3 take away 3 x^3
how many x^3 ?
(it's harder with negative numbers, but if it were positive numbers, and cows instead of x's it would be easier).
-3 x^3 + -3x^3 becomes ??

Answer 28

if it were 3x^3 + 3x^3 that would mean
3 x^3 plus another 3 x^3, or 6 x^3 all together
with the minus signs we do -3 + -3 to get -6 x^3

Answer 29

Ah I see so you combined them.

Answer 30

yes. so now you have
5x^4 -6x^3
now look for all the terms with x^2 . See any ?

Answer 31

Yes 11x^2

Answer 32

yes. and there is only that one term, so write that down.
now look for x^1 terms (remember x^1 is the same as x)

Answer 33

8x

Answer 34

I see another one. do you see it ?

Answer 35

6x

Answer 36

now we have 8 x's and 6 x's. how many x's do we have ?

Answer 37

2 ?

Answer 38

you have 8 cows in the barn and 6 cows in the pasture. how many cows?

Answer 39

14 Cows? lol

Answer 40

yes. the same idea works for x's
you have
8x + 6x

Answer 41

Ohhhhhhh so 14x Right?

Answer 42

We combine them like beforer!

Answer 43

yes
now write that last part and we get the entire answer
\[ 5x^4 -6x^3 -11x^2 +14x \]

Answer 44

Woah! I get it!

Answer 45

It may seem boring, but it's good to figure this stuff out. It turns out to help you think.

Answer 46

Of course now I have to show my work... lol

Answer 47

showing the work means:
write the original problem.
then write what you get after "distributing" the -1 (see up above)
then write the terms down in "order"
then combine "like terms" and write the final answer.

Answer 48

Oh, of course. I see now. Thank you greatly!! @phi This is my very last question for my entire schooling!! When I submit this answer I will finally graduate! So you were the one that helped me do the very last question of my entire schooling! 12 grades done! Thank you.