因式分解写过程

(a+b)^3+(a-b)^3-8a^3
=[(a+b)+(a-b)][(a+b)^2-(a+b)(a-b)+(a-b)^2]-8a^3
=2a[a^2+2ab+b^2-(a^2-b^2)+a^2-2ab+b^2]-8a^3
=2a[a^2+3b^2]-8a^3
=2a^3+6ab^2-8a^3
=6ab^2-6a^3
=6a(b^2-a^2)
=6a(b+a)(b-a)

(x+1)(x+2)(x+3)(x+6)+x^2
=[(x+1)(x+6)][(x+2)(x+3)]+x^2
=(X^2+7X+6)(X^2+5X+6)+X^2
=[(X^2+6)+7X][(X^2+6)+5X]+X^2
=(X^2+6)^2+12X(X^2+6)+35X^2+X^2
=(X^2+6)^2+2*6X*(X^2+6)+36X^2
=(X^2+6X+6)^2

(x^2+3x+2)(x^2+7x+12)-120
=(x+1)(x+2)(x+3)(x+4)-120
=[(x+1)(x+4)][(x+2)(x+3)]-120
=(x^2+5x+4)(x^2+5x+6)-120
=(x^2+5x)^2+10(x^2+5x)+24-120
=(x^2+5x)^2+10(x^2+5x)-96
=[(x^2+5x)+16][(x^2+5x)-6]
=(x^2+5x+16)(x^2+5x-6)
=(x^2+5x+16)(x+6)(x-1)

(a+b)^3+(a-b)^3-8a^3
=2A^3+6B^2A-8A^3
=6B^2A-6A^3
=6A(B+A)(B-A)

(X+1)(X+2)(X+3)(X+6)+X^2
=(X^2+7X+6)(X^2+5X+6)+X^2
=[(X^2+6)+7X][(X^2+6)+5X]+X^2
=(X^2+6)^2+12S(X^2+6)+35X^2+X^2
=(X^2+6)^2+2