Question

分解因式

分解因式 （x+y)²-6x(x+y)+9x² a³-2a²+a 4xy²-4x²y-y³ (x-2y)²+8xy (x²+4)²-16x²

Answer 1

（x+y)²-6x(x+y)+9x²
=(x+y-3x)²
=(y-2x)²
a³-2a²+a
=a(a² -2a+1)
=a(a-1)²
4xy²-4x²y-y³
=-y(-4xy+4x² +y² )
=-y(2x-y)²
(x-2y)²+8xy
=x²-4xy+4y²+8xy
=x²+4xy+4y²
=(x+2y)²
(x²+4)²-16x²
=(x²+4+4x)(x²+4-4x)
=(x+2)²(x-2)²

愿对你有所帮助！

Answer 2

（x+y)²-6x(x+y)+9x²
=(x+y-3x)²
=（y-2x)²

a³-2a²+a
=a(a²-2a+1)
=a(a-1)²

4xy²-4x²y-y³
=-y(4x²-4xy+y²)
=-y(2x-y)²

(x-2y)²+8xy
=x²-4xy+4y²+8xy
=x²+4xy+4y²
=(x+2y)²

(x²+4)²-16x²
=(x²+4-4x)(x²+4+4x)
=(x-2)²(x+2)²

Answer 3

（x+y)²-6x(x+y)+9x²
=x²+2xy+y²-6x²-6xy+9x²

=4x²-4xy+y²
=(2x-y)²

a³-2a²+a

=a(a²-2a+1)
=a(a-1)²

4xy²-4x²y-y³
=y(4xy-4x²-y²)
=-y(y-2x)²

Answer 4

(y-2x)^2
a(a-1)^2
-y(2x-y)^2