Factorize(1+x)^4 - (1-x^2)^2

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

=[(1+x)^2]^2 - (1-x^2)^2

=[(1+x)^2+(1-x^2)][(1+x)^2-(1-x^2)]

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

=(2x+2)(2x^2+2x)

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

=4x(x+1)(x+1)

=4x(x+1)^2


2008-02-03 12:33:37 補充：
Remark: a^2 - b^2 = ( a + b )( a - b )