①3x²+6xy+3y²②81(m+n)²-16(m-n)²③4x²(x-y)+(y-x)

题目

①3x²+6xy+3y²②81(m+n)²-16(m-n)²③4x²(x-y)+(y-x)
④16x的四次方-8x²y²+y四次方
⑤x²y的n-1次方-y的n+1次方
⑥-4a²x²+8ax-4
⑦x²-y²-2x+2y
⑧4x²-y²-4x+1

答案

①3x²+6xy+3y²
=3(x²+2xy+y²)
=3(x+y)²
②81(m+n)²-16(m-n)²
=[9(m+n)]²-[4(m-n)]²
=(9m+9n+4m-4n)(9m+9n-4m+4n)
=(13m+5n)(5m+13n)
③4x²(x-y)+(y-x)
=4x²(x-y)-(x-y)
=(x-y)(4x²-1)
=(x-y)(2x+1)(2x-1)
④16x的四次方-8x²y²+y四次方
=(4x²-y²)²
=(2x+y)²(2x-y)²
⑤x²y的n-1次方-y的n+1次方
=y的(n-1)次方(x²-y²)
=y的(n-1)次方(x+y)(x-y)
⑥-4a²x²+8ax-4
=-4(a²x²-2ax+1)
=-4(ax-1)²
⑦x²-y²-2x+2y
=(x+y)(x-y)-2(x-y)
=(x-y)(x+y-2)
⑧4x²-y²-4x+1
=(4x²-4x+1)-y²
=(2x-1)²-y²
=(2x-1+y)(2x-1-y)