Someone work out this algebra problem?

Question

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

The answer is 6x^2 +2

(^ means exponent)

I keep getting 4x^2 + 6 as my answer and thats obviously not right. This is how I did it, can you tell me what I'm doing wrong?

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

(x+1)(x+1)(x+1) - (x-1)(x-1)(x-1)

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

x^3 + 2x^2 +x +3 - x^3 + 2x^2 - x +3

4x^2 + 6

so what am i not seeing?

thanks (=

Answer 1

Remember to multiply -1 times the second term b4 expanding the exponent.

Change (x+1)^3-(x-1)^3 to (x+1)^3+(-x+1)^3 & then expand and solve

Answer 2

1 x 1 = 1  not 3

Answer 3

(x^2 + 2x +1)(x+1)

= x^3 + 2x^2 + x

+ x^2 + 2x +1

= x^3 + 3x^2 + 3x + 1

Also,

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

= x^3 - 2x^2 + x

- x^2 + 2x - 1

= x^3 - 3 x^2 + 3x - 1

Subtract them and get 6 x^2 + 2

Answer 4

The answer: 6x^2 + 2 is right!

There are two mistakes you had made:

(x + 1)^3 = (x + 1)(x +1)(x + 1)

= (x ^2 + 2x + 1)(x + 1)

= x^3 + 2x^2 + x + x^2 + 2x + 1

=x^3 + 3x^2 + 3x + 1       (1)     (this is your 1st mistake)

Same as:

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

= x^3 - 2x^2 + x - x^2 + 2x - 1

= x^3 - 3x^2 + 3x -1        (2)    (this is your 2nd mistake)

Subtract (1) and (2) you will have:

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

= x^3 + 3x^2 + 3x + 1 - 3x^3 + 3x^2 - 3x + 1

= 6x^2 + 2   is the answer.

Or if you know the formual

(a + b)^3 = a^3 + 3x^2 + 3x +1

(a - b)^3  =  a^3 - 3x^2 + 3x - 1

Your work would be easier!

Good Luck!

Answer 5

It looks like in your fourth step above you are missing some terms.

after you multiply in your third step, it should look like this:

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

x^3 + 3x^2  +  3x  + 1   -  x^3  +  3x^2  -  3x  +  1

add the terms = 6x^2  +  2

Answer 6

You are good down to

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

This expands to

x^3+2x^2+x  +X^2+2X+1, not only +3

You didn't distribute the +1 to all 3 terms in

(x^2+2x+1)

Likewise for (x^2-2x+1)(x-1)

This becomes x^3-2x^2+x-x^2+2x-1

You thus get

x^3+2x^2+x+x^2+2x+1 -

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

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

=x^3+3x^2+3x+1-x^3+3x^2-3x+1

=6x^2+2

Answer 7

(x+1)^3 = x^3 + 3x^2 + 3x + 1

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

Subtract:  6x^2 + 2