Question

因式分解 a(a-1)(a-2)-6 （x+2)(x-2)-4y(x-y) y(y+2)+4x(x-y-1) 9(a+c)(a-c)-b(b+6c)

Answer 1

a(a-1)(a-2)-6
=a(a-1)(a-2)+6[(a-3)-(a-2)]
=(a-2)[a(a-1)-6]+6(a-3)
=(a-2)(a²-a-6)+6(a-3)
=(a-2)(a-3)(a+2)+6(a-3)
=(a-3)(a²+2)

(x+2)(x-2)-4y(x-y)
=x²-4-4xy+4y²
=(x-2y)²-4
=(x-2y+2)(x-2y-2)

y(y+2)+4x(x-y-1)
=y²+2y+4x²-4xy-4x
=(y-2x)²-2(y-2x)
=(y-2x)(y-2x-2)
=(2x-y)(2x-y+2)

9(a+c)(a-c)-b(b+6c)
=9a²-9c²-b²-6bc
=9a²-(b+3c)²
=(3a+b+3c)(3a-b-3c)

Answer 2

a(a-1)(a-2)-6
=a(a^2-2a-a+2)-6
=a^3-3a^2+2a-6
=a^2(a-3)+2(a-3)
=(a-3)(a^2+2)

（x+2)(x-2)-4y(x-y)
=x^2-4-4xy+4y^2
=(x^2-4xy+4y^2)-4
=(x-2y)^2-4
=(x-2y+2)(x-2y-2)

y(y+2)+4x(x-y-1)
=y^2+2y+4x^2-4xy-4x
=(4x^2-4xy+y^2)-(4x-2y)
=(2x-y)^2-2(2x-y)
=(2x-y)(2x-y-2)

9(a+c)(a-c)-b(b+6c)
=9(a^2-c^2)-b^2-6bc
=9a^2-9c^2-b^2-6bc
=9a^2-(9c^2+6bc+b^2)
=9a^2-(3c+b)^2
=(3a+3c+b)(3a-3c-b)