Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Difference of Cubes

Copy and paste thus url to see question.

https://imgur.com/a/ZSarUyQ

Bob

Administrator

Registered: 2010-06-20

Posts: 10,475

Re: Difference of Cubes

If you graph this as a function you'll see it only crosses the x axis once so this will factorise into a linear factor and a quadratic one which won't further factorise in real numbers.

Maybe you're confused because you have used x to mean two different things. Let's avoid this by using y and b for the identity:

So y = 3x - 2 and b = 3.  This will give you the linear factor and the quadratic cannot be simplified further.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Difference of Cubes

If you graph this as a function you'll see it only crosses the x axis once so this will factorise into a linear factor and a quadratic one which won't further factorise in real numbers.

Maybe you're confused because you have used x to mean two different things. Let's avoid this by using y and b for the identity:

So y = 3x - 2 and b = 3.  This will give you the linear factor and the quadratic cannot be simplified further.

Bob

There is no difference between the formula you provided and the textbook x^3 - a^3 = (x - a)(x^2 + ax + a^2). So, I don't understand your comment about me being confused. I didn't go further in my work.

Let x = (3x - 2)

Let a = 3

When I plug this into your formula and Sullivan's formula, I get stop when I see the answer is something completely different that the answer posted in the back of the textbook.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Difference of Cubes

There is no difference between the formula you provided and the textbook x^3 - a^3 = (x - a)(x^2 + ax + a^2). So, I don't understand your comment about me being confused. I didn't go further in my work.

Let x = (3x - 2)

the line above is where you use "x" to mean 2 different things: the placeholder in the factorisation formula and also the variable from the original expression

taken literally it says

When I plug this into your formula and Sullivan's formula, I get stop when I see the answer is something completely different that the answer posted in the back of the textbook.

weird
what are you getting?

let formula be

you have

so plug in

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Difference of Cubes

https://i.imgur.com/YzIqVO3.jpeg

There is no difference between the formula you provided and the textbook x^3 - a^3 = (x - a)(x^2 + ax + a^2). So, I don't understand your comment about me being confused. I didn't go further in my work.

Let x = (3x - 2)

the line above is where you use "x" to mean 2 different things: the placeholder in the factorisation formula and also the variable from the original expression

taken literally it says

When I plug this into your formula and Sullivan's formula, I get stop when I see the answer is something completely different that the answer posted in the back of the textbook.

weird
what are you getting?

let formula be

you have

so plug in

Copy and paste to see my work and answer.

https://imgur.com/a/SARLc54

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Difference of Cubes

...my work and answer.

looks good to me
also they both multiply out to the same thing

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Difference of Cubes

...my work and answer.

https://i.imgur.com/TZdv1iQ.jpeg

looks good to me
also they both multiply out to the same thing

Did you post my picture?
I don't recall posting this picture.
My cell phone does not accept imgur for some strange reason.