s1-s2~maths

1 a) (x+y)(x^2-xy+y^2) = x^3+y^3

1 b) (x-y)(x^2+xy+y^2) = x^3-y^3

2. (x^2+x+1)(x^2-x+1) = (x^2+1+x)(x^2+1-x)

Consider x^2+1 = a and x = b

Because (a+b)(a-b) = a^2-b^2

Therefore (x^2+1+x)(x^2+1-x) = (x^2+1)^2-x^2 = x^4+2x^2+1-x^2 = x^4+x^2+1

2007-08-19 12:24:32 補充：
1 a) and b) is actually a formulabut if we need, we can expand it like this:(x y)(x^2-xy y^2) = x(x^2-xy y^2) y(x^2-xy y^2) = (x^3-x^2y xy^2) (x^2y-xy^2 y^3) = x^3 y^3(x-y)(x^2 xy y^2) = x(x^2 xy y^2) - y(x^2 xy y^2) = (x^3 x^2y xy^2) - (x^2y xy^2 y^3) = x^3-y^3