Question

一道简单的因式分解分解因式:(X+1)(x+2)(X+3)-6*7*8原式=(x+2-1)(X+2)((X+2+1)-(

Answer 1

=(x+2-1)(（X+2)(X+2+1)-(7-1)*7*(7+1)

=[(x+2-1)(X+2+1)(X+2)-(7-1)*(7+1)*7(这步中将x+2,7看成一个数,用平方差公式)

=[(X+2)^2-1]*(X+2)-(7^2-1)*7

=(X+2)^3-(X+2)-7^3+7

=(X+2-7)[(X+2)^2+7(X+2)+7^2]-(x-5)(相当于a^3-b^3)

=(x-5)[(x+2)²+7(x+2)+7²-1]

= (X-5)(X^2+11X+66)