Question

几道因式分解题

4X的四次方+1

X的三次方-3X+2

(X+Y-2XY)(X+Y-2)+(XY-1)²

(X+1)(X+2)(X+3)(x+6)+X²

X-2Y=8/2007

2X+Y=2007/3 不解方程组,求9X²-15XY-6Y²的值

Answer 1

4X的四次方+1
=4x^4+4x^2+1-4x^2
=(2x^2+1)^2-4x^2
=(2x^2+2x+1)(2x^x-2x+1)

X的三次方-3X+2
=x^3-1-3x+3
=(x-1)(x^2+x+1)-3(x-1)
=(x-1)(x^2+x+1-3)
=(x-1)^2(x+2)

(X+Y-2XY)(X+Y-2)+(XY-1)²
=(x+y)²-2(x+y)-2xy(x+y)+4xy+x²y²-2xy+1
=(x+y)²-2xy(x+y)+x²y²+2xy-2(x+y)+1
=(x+y-xy)²-2(x+y-xy)+1
=(x+y-xy-1)²
=(y-1)²(1-x)²

(X+1)(X+2)(X+3)(x+6)+X² 14相乘 23相乘
=(x²+7x+6)(x²+5x+6)+x²
=(x²+6)²+12x(x²+6)+36x²
=(x²+6x+6)²

X-2Y=8/2007

2X+Y=2007/3 修改为3x+y
不解方程组,求9X²-15XY-6Y²的值
9x²-15xy-6y²
=3(3x²-5xy-2y²)=3(3x+y)(x-2y)=8