SOLUTION: When factoring the problem (x+1)^3 - 27x^3 I use the Difference of Cubes (a-b)(a^2 + ab + b^2) to get (x+1-3x)((x+1)^2 + (x+1)*(3x) + (3x)^2). I understand all of this so far.

Algebra ->  Exponents -> SOLUTION: When factoring the problem (x+1)^3 - 27x^3 I use the Difference of Cubes (a-b)(a^2 + ab + b^2) to get (x+1-3x)((x+1)^2 + (x+1)*(3x) + (3x)^2). I understand all of this so far.      Log On


   

Question 319974: When factoring the problem (x+1)^3 - 27x^3 I use the Difference of Cubes (a-b)(a^2 + ab + b^2) to get (x+1-3x)((x+1)^2 + (x+1)*(3x) + (3x)^2). I understand all of this so far. When I simplify I understand everything except how (x+1)^2 is equal to (x^2 + 2x + 1). The solution is: (-2x+1)(13x^2 +5x +1).
can you explain to me why (x+1)^2 = (x^2 + 2x + 1).
^ = exponent.
Thank You
Don
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You use the FOIL method to get: %28x%2B1%29%5E2=%28x%2B1%29%28x%2B1%29=x%5E2%2Bx%2Bx%2B1=x%5E2%2B2x%2B1 which means that %28x%2B1%29%5E2=x%5E2%2B2x%2B1