Question

Simplify 7(2x+1)^3-(2x+1)^4

Answer 1

your best bet is to write it as
\[7(2x+1)^3-(2x+1)(2x+1)^3\] and then factor
otherwise it will be a large mess

Answer 2

7(2x^3+1)-(2x+1)(2x^3+1)

Answer 3

right so far?

Answer 4

Yeah you can also think of it like this,
7y^3-y^4
so
y^3(7-y)
(2x+1)^3(7-(2x+1))
(2x+1)^3(6-2x)

Answer 5

7(2x^3+1)-(2x+1)(2x^3+1)

14x^3+7-(4x^4+2x+2x^3+1)

Answer 6

im struggling with the right side

Answer 7

From \(7(2x^3+1)-(2x+1)(2x^3+1)\)
you missed the cubed for 2x+1,
Should be like this,
\[7(2x+1)^3-(2x+1)(2x+1)^3\]
Simplifying or factoring,
\[(2x+1)^3(7-(2x+1))\]
\[(2x+1)^3(6-2x)\]
Factor 2 out
\[2(2x+1)^3(3-x)\]

Answer 8

im not following u

Answer 9

or, because I don't like (3-x), factor out -1 form (3-x) to get -1*(x-3)
\[ -2(2x+1)^3(x-3) \]

Answer 10

can u please show me step by step how to solve this problem

Answer 11

7(2x^3+1)-(2x+1)(2x^3+1)
right so far?

no, this does not match the original
you want
7(2x+1)^3 - (2x+1)(2x+1)^3
where you have the exponent of 3 on the everything in the parens

Answer 12

what do u mean doesnt match the original?

Answer 13

as posted above, if you rename (2x+1)^3 as y (so we can see the pattern)
you would have
7*y -(2x+1)*y

can you factor y from each term?

Answer 14

ok i gotcha so u should look to have the same exponent

Answer 15

wouldnt that be 7y-2x-1*y

Answer 16

Let's start at the beginning
7(2x+1)^3-(2x+1)^4

rename (2x+1) as y (no exponent, so this is different from what I did up above)
replace (2x+1) with y:
7*y^3 - y^4

follow?

Answer 17

now write y^4 as y*y^3 (remember y^1 * y^3 = y^(1+3) = y^4 add exponents)

Answer 18

yes i follow

Answer 19

so rewrite y^4 as y*y^3 to get
6*y^3- y*y^3

y^3 is in both terms, so it can be "factored out"
what do you get?

Answer 20

u mean 7*y^3

Answer 21

y^3(7-y)

Answer 22

yes, 7y^3-y*y^3

looks good:
y^3(7-y)

now replace y with (2x+1)
what do you get?

Answer 23

(2x+1)^3(7-(2x+1))

Answer 24

good. notice that (7-(2x+1)) is the same as (means) (7+ -1*(2x+1))
distribute the -1 by multiplying it times each term in the parens

Answer 25

(2x+1)^3*(7-2x-1)

Answer 26

now combine "like terms" in the 2nd parens: you have (reordering and making it all addition)
+7 + -2x + -1 or -2x + 7 + -1

Answer 27

(2x+1)^3*(6-2x)

Answer 28

(2x^3+1)*(6-2x)

12x^3-4x^4+6-2x

=-4x^4+12x^3-2x+6

Answer 29

no, expanding this is messy. we can do that later (because you are not doing it correctly, and it is good to know how), but for now, the thing to do is
factor -2 out of the last parens: (6-2x)

Answer 30

(2x^3+1)*-2(6+x)

Answer 31

lost the bubble, after all those correct steps!

Here is where you were
(2x+1)^3*(6-2x)

first, do not do anything to the first term (2x+1)^3
for the other term, notice that both terms inside can be divided by -2:
6= -2*-3 and -2*x is -2*x: so (6+ -2x) is the same as (-2* -3 + -2*x)
there is a -2 in each.
can you factor it out?

Answer 32

(2x+1)^3*(6-2x)

(2x+1)^3*-2(-3+x)

Answer 33

yes, now people put the -2 out front, rather than in the middle
also, people like the x term first in that 2nd parens
so, the standard way to write this is:
-2(2x+1)^3 (x-3)

follow?

Answer 34

yes

Answer 35

(-3+x) is the same as (x+ -3) (you can switch the order when adding)
and (x+ -3) is generally written as (x-3) (looks simpler)

Answer 36

okay

Answer 37

-2(2x+1)^3 (x-3)
is the answer

though if it were multiple choice, you might see
-2(x-3)(2x+1)^3
(different order, but the same thing, just like 2*3*4 is the same as 3*4*2)

Answer 38

the answer should be 2(2x+1)^3(3-x)

Answer 39

Now just a note on (2x+1)^3

the exponent 3, written as
\[ (2x+1)^3 \]
is short hand for multiplying the "base" (which is (2x+1) here)
by itself 3 times.
so, you could write
\[ (2x+1)^3 =(2x+1)(2x+1)(2x+1)\]

Answer 40

how would u go about multiplying that out

Answer 41

you could use foil to multiply
(2x+1)(2x+1) to get 4x^2+4x+1
then you have to multiply by (2x+1) again!
( 4x^2+4x+1)(2x+1) =
2x^3+8x^2+2x+4x^2+4x+1 which simplifies to
2x^3 + 12x^2 +6x+ 1

as you can see, it is messy. Now the trick is if you started with this
2x^3 + 12x^2 +6x+ 1

can you figure out it is (2x+1)^3 ?! (that is the hard to do!)