Question

Use binomial expansion to expand:
(1 + x + x²)²
noting that 1 + x + x² = 1 + ( x + x² )

Answer 1

x^4+2x^3+3x^2+2x+1

Explanation:

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

use the binomial expansion for second degree. Pascal's triangle would give coefficients 1 2 1

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

use binomial expansion again on the last component

-> 1+2x+2x^2+(x^2+2x^3+x^4)

finally, expand

-> 1+2x+2x^2+x^2+2x^3+x^4

=x^4+2x^3+3x^2+2x+1