将下列各式进行因式分解1.abx²-(ac-b²)x-bc2.(ax+by)²+(bx-ay)²3.x⁴+4请写出具体的步骤,

Question

将下列各式进行因式分解
1.abx²-(ac-b²)x-bc
2.(ax+by)²+(bx-ay)²
3.x⁴+4
请写出具体的步骤,

Answer 1

1.
=abx^2-acx+b^2x-bc
=ax(bx-c)+b(bx-c)
=(bx-c)(ax+b)
2.
=(ax)^2+(by)^2+2abxy+(bx)^2+(ay)^2-2abxy
=a^2(x^2+y^2)+b^2(x^2+y^2)
=(x^2+y^2)(a^2+b^2)
3.
=x^4+4-4x^2+4x^2
=(x^2+2)^2-4x^2
=(x^2+2-2x)(x^2+2+2x)