Question

几道因式分解的题目~

4(x-y+1)+y(y-2x)

4x^4-13x²+9

过程希望详细``

Answer 1

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

4x^4-13x²+9
=(x^2-1)(4x^2-9)
=(x-1)(x+1)(2x-3)(2x+3)

Answer 2

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

4x^4-13x²+9
=4x^4-12x^2+9-x^2
=(2x^2-3)^2-x^2
=(2x^2-3+x)(2x^2-3-x)
=(2x+3)(2x-3)(x+1)(x-1)

Answer 3

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

4x^4-13x²+9
=4x^4-12x^2+9-x^2
=(2x^2-3)^2-x^2
=(2x^2-3+x)(2x^2-3-x)
=(2x+3)(2x-3)(x+1)(x-1) 仅供参考

Answer 4

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

4x^4-13x^2+9
=(4x^2-9)(x^2-1)
=(2x+3)(2x-3)(x+1)(x-1)