Question

因式分解，②和③要求在实数范围内

①（x-y）³+4（y-x）
②x^4-4
③6x²-4

Answer 1

1, =(x-y)^3-4(x-y)
=(x-y)[(x-y)^2-4]
=(x-y)(x-y+2)(x-y-2)
2, =(x^2)^2-2^2
=(x^2+2)(x^2-2)
=(x^2+2)(x+√2)(x-√2)
3,=(√6x)^2-2^2
=(√6x+2)(√6x-2)

Answer 2

①（x-y）³+4（y-x）

=(x-y)[(x-y)^2-4]
=(x-y)(x-y+2)(x-y-2)
②x^4-4
=(x^2+2)（x^2-2)
③6x²-4

=2(3x^2-2)

Answer 3

(x-y)^3+4(y-x)=(x-y)^3-4(x-y)=(x-y)[(x-y)^2-4]=(x-y)(x-y+2)(x-y-2)
x^4-4=(x^2+2)(x^2-2)=(x^2+2)(x+√2)(x-√2)
6x^2-4=(√6x+2)(√6x-2)

Answer 4

1.（x-y)（x-y-4)

2. （X的平方+2）（x-2)(x+2)

3. 2(3x的平方-2）