Question

Hey plz help
(X-4)^3
I know the cube rule
(X-4) (x^2+4x+16)
I have to expand and simplify so
I am getting X^3-64
But the answer is
X^3-12x^2+48x-64
I think i dunno some rule

Answer 1

I think that when multiplying your doing a sign error. Like for example your replacing a minus with a plus and things like that.

A couple of reminders:
-(x+6) = -x - 6,
(-x)(-y) = xy
(x)(y) = xy
(-x)(y) = (-xy)
(x)(-y) = (-xy)


I used to do these mistakes so I totally understand what your currently going though.

Hope this helps.

Answer 2

@Boblovesmath thank u but i tried again it didnt help
(X-4)(x^2+4x+16)
X^3+4x^2+16x-4x^2-16x-64
X^3-64

Answer 3

@dan815 can u plz help me i am sure u know it only for a sec plz

Answer 4

do you know the distributive property?
a(b+c)= ab + ac

you can use that idea with your problem
(x-4) (x^2+4x+16)

distribute the (x-4) (multiply each term inside the parens by (x-4) )
what do you get ?

Answer 5

X^3 -64

Answer 6

See above^

Answer 7

no. Just write down (x-4) times each term inside the parens
do not simplify (yet)
what do you get ?

Answer 8

U mean (x-4)x^2 +(x-4)4x+(x-4)16

Answer 9

yes, looks good.

Answer 10

now notice for the first term that you wrote
(x-4)x^2 or x^2(x-4)
we can distribute the x^2
can you do that ?

Answer 11

X^3-4x^2

Answer 12

ok, now do the 2nd term
(x-4)4x (we can distribute the 4x)

Answer 13

4x^2-16

Answer 14

and the last term
(x-4)16

Answer 15

16x-64

Answer 16

X^3-4x^2 + 4x^2-16 +16x -64

Answer 17

Yea

Answer 18

4x^2-16x*

Answer 19

I think we would get the correct answer if we started with
(x-4)(x-4) = x(x-4) + -4(x-4) = x^2 -4x -4x +16 = x^2 -8x +16

now do
(x-4)( x^2 -8x +16)

Answer 20

(X-4) ^3 is cube why u put only two brackets of (x-4)

Answer 21

It's easier to see what I did if we say
A(x-4) = xA + -4A

and then say, A is short for the first (x-4)
x(x-4) + -4(x-4)

Answer 22

**only two brackets of (x-4)

because I am doing it in steps:

(x-4) * ( (x-4)(x-4) )

the (x-4)(x-4) = x^2 -8x +16

I redid that because up top you wrote
***
I know the cube rule
(X-4) (x^2+4x+16)
***

and that is not correct.

Answer 23

if we use the correct (x-4)(x-4) = x^2 -8x +16

we can now do
(x-4)(x^2 -8x +16)

and it will turn out to be
\[ x^3-4x^2 -8x^2 +32x +16x -64 \\
x^3 -12x^2 +48x -64
\]

Answer 24

Oh thank u thank u