Question

Problem: (5x^4 – 3x^3 + 6x) – (3x^3 + 11x^2 – 8x)

Answer: 5x^4-6x^3 -11x^2 +14x

Can you show me how to solve it? Show your work! Work it out!
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Answer 1

Are those powers/exponents?

Answer 2

powers sorry

Answer 3

(5x^4-3x^3+6x)-(3x^3+11x^2-8x)
distribute negative to the second group
(5x^4-3x^3+6x)-3x^3-11x^2+8x
combine like terms
5x^4-3x^3-3x^3-11x^2+6x+8x
add like terms
5x^4-6x^3-11x^2+14x

Answer 4

find all the terms the have x to the same exponent, and "combine" those terms

Answer 5

the first tricky part is this
– (3x^3 + 11x^2 – 8x)

the "-" sign out front means -1 * (3x^3 + 11x^2 – 8x)
and that means -1 times each term inside the parens

Answer 6

so you would multiply -1 times each term inside the parens. You should get
-1 * (3x^3 + 11x^2 – 8x)
becomes
-1*3*x^3 + -1*11*x^2 + -1* -8 * x

Answer 7

people would simplify
-1*3*x^3 + -1*11*x^2 + -1* -8 * x
by doing -1*3 is -3
so the first term is
-3*x^3 or just -3x^3 (we usually leave out the multiply sign)
can you do the there two terms?

Answer 8

can you simplify
-1*11*x^2
?

Answer 9

-11x^2

Answer 10

@phi

Answer 11

yes

Answer 12

and this one
-1* -8 * x
?

Answer 13

8x

Answer 14

yes
so you should know how to change
– (3x^3 + 11x^2 – 8x)
into

-3x^3 -11x^2 + 8x

Answer 15

and we use that to write
(5x^4 – 3x^3 + 6x) – (3x^3 + 11x^2 – 8x)

as (notice we can drop the parens):
5x^4 – 3x^3 + 6x – 3x^3 - 11x^2 + 8x

Answer 16

now you look for the term with the biggest exponent. It is 5x^4
there is only one term with exponent 4.
we write down

5x^4

next we look for the terms with the next biggest exponent.
what terms do we find ?

Answer 17

what terms in
5x^4 – 3x^3 + 6x – 3x^3 - 11x^2 + 8x

have x with an exponent of 3 ? (and include the sign)

Answer 18

3x^3

Answer 19

-3x^3 (don't forget the minus sign)
and there is another x^3 term, right ?

Answer 20

yep

Answer 21

you should find
-3x^3 - 3x^3

you have -3 of x^3 plus another -3 of x^3
(it's tougher to explain with negative numbers, but we "add the coefficients"
in this case -3+ -3 = -6 of x^3

in other words
-3x^3 - 3x^3 = -6x^3

so far we have
5x^4 -6x^3

now look for all terms with x^2
what do you find ?