Question

4道因式分解。

①4x²+2x+y+y²+4xy
②x²-y²+4y-1
③16x²-24xy-1+9y²
④4x²-16xy+4y²-6x+6y
全部要过程。谢了 。谢了。 - -

Answer 1

①4x²+2x+y+y²+4xy
= 4x²+4xy+y²+2x+y
= (2x+y)²+2x+y
= (2x+y)(2x+y+1)

②抄错题了，应为x²-4y²+4y-1
x²-4y²+4y-1
= x²-(2y-1)²
= (x+2y-1)(x-2y+1)

③16x²-24xy-1+9y²
= 16x²-24xy+9y²-1
= (4x-3y)²-1
= (4x-3y+1)(4x-3y-1)

④抄错题了，应为4x²-8xy+4y²-6x+6y
4x²-8xy+4y²-6x+6y
=2(x²-2xy+y²)-6(x-y)
= 2(x-y)²-6(x-y)
= 2(x-y)(x-y-3)

Answer 2

①4x²+2x+y+y²+4xy
=4x²+4xy+y²+2x+y
=(2x+y)²+(2x+y)
\(2x+y)(2x+y+1)

②x²-y²+4y-1
不能分解
换一个x²-y²+4y-4
=x²-(y-2)²
=(x+y-2)(x-y+2)

③16x²-24xy-1+9y²
=16x²-24xy+9y²-1
=(4x-3y)²-1
=(4x-3y+1)(4x-3y-1)

④4x²-16xy+4y²-6x+6y
这个题目似乎也有问题