a^3+b^3 (1 Viewer)

[AntiJap]

hai guys is the expansion of a^3+b^3=(a+b)(a^2+ab+b^2)
how do you determine the sign of the term in bold?

thanks

 

[acmilan]

a³ + b³ = (a+b)(a² - ab + b²)
a³ - b³ = (a-b)(a² + ab + b²)

Negative when its the sum of cubes, positive when its difference of cubes

 

[k8kate]

The first bracket is just (a+b) or (a-b). The sign in the 1st bracket is the same as in the original.

The second bracket is square the first term, square the last term, times the terms together double it and change the sign.

If you understand that.

 

[Slidey]

If the expression is blah-cubed PLUS blah-cubed, the ab is MINUS. Otherwise it is plus. In other words.

 

[hyparzero]

a^3 + b^3 = Window

 

[JhK89]

if u want to know what the bold part is u just multiply the values in the first bracket ^^ but look at the 2nd post for the sings there is onli 1 "-" in the thingy..

 

[fishy89sg]

if the expansion doesnt match the identity, you know you did something wrong

 

[Affinity]

to determine the sign you expand and check.. after a few hundred times it will be obvious
by the way it's a^3 + b^3 = (a + b)(a^2 - ab + b^2)

 

[PC]

Now I'm confused!

OK ... it's:
a³ + b³ = (a + b)(a² – ab + b²)
and
a³ + b³ = (a – b)(a² + ab + b²)

So we have to remeber that the first term is just a and b, and it's positive or negative depending on the original expression. The second term is always a², ab and b². The squares are always positive, and the sign of the ab is the opposite of the original expression.

In other words, there is always a negative in there somewhere. Either at the start, or in the middle.

 

[pLuvia]

I think you meant
a³+b³=(a+b)(a²-ab+b²)

a³-b³=(a-b)(a²+ab+b²)

 

[k8kate]

Ya you really fucked that up.