I need to simplify (x^3+1)^2 as part of a question I am doing. I think this answer is x^12+1, but I am unsure. Also 12x(x^3+1) needs simplified and I think I am correct in thinking it is 12x^4 + 12x

1st one isn't correct

(x^3+1)^2

Think of it as (xxx+1)(xxx+1)

2nd one is fine.

To expand it, just type it like...

( x ^ 3 + 1 ) ^ 2

(Sorry, couldn't resist ;)). OK, one approach that's easy to remember is to first re-express it as

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

... and then apply the "FOIL" method; you remember, multiply the first two terms, the outer two terms, the inner two terms, and the last two terms.

That method gives a general formula for any two numbers a and b:

(a + b)^2 = (a + b)(a + b) = a^2 + 2ab + b^2

Give it a whirl.

um.. . I get (x^6)+(2x^3)+1.. . But it has been a few years.. . Expand with foil (Firsts, Inners, Outers, Lasts)
so my working out if you can follow it is.. .
(x^3+1)(x^3+1)
(x^3)^2 +(x^3) +(x^3)+1
X^6+(2X^3)+1

if you substitute X with a value such as 2 you come out with the same answer at the beginning as you do at the end so that's a good sign that its still the same equation :)

Actually, it's not an equation. It's an expression. An equation has an equals sign and we are directed to solve for something. In this case, expansion is the issue. No equals sign. Therefore, an expression.
Just letting you know the difference if you didn't already.

Equation: (x^{3}+1)^{2}=0

Expression: (x^{3}+1)^{2}

1st one isn't correct

(x^3+1)^2

Think of it as (xxx+1)(xxx+1)

2nd one is fine.

Thanks for your reply.

um . . . i get (x^6)+(2x^3)+1 . . . . . but it has been a few years . . . . expand with foil (Firsts, Inners, Outers, Lasts)
so my working out if you can follow it is . . . ..
(x^3+1)(x^3+1)
(x^3)^2 +(x^3) +(x^3)+1
X^6+(2X^3)+1

if you substitute X with a value such as 2 you come out with the same answer at the beginning as you do at the end so thats a good sign that its still the same equation :)


Just realised where I'd made the mistake after using FOIL method before posting my question, I add the x^3 + x^3 and stupidly got x^6, when it should as you rightly say 2x^3. Thanks for all replies.