已知x+y=4,xy=7,则x²+y²=_____,x²y+xy²_____.

题目

已知x+y=4,xy=7,则x²+y²=_____,x²y+xy²_____.
18b（a-b）²-12（b-a）三次方
x三次方-16xy²
18a-12ax+2ax²
x²-5x-24
am-2bm-2bm+an
（a²+4b²）²-16a²b²

答案

1已知x+y=4,xy=7,则x²+y²=(x+y)²-2xy=16-14=2,x²y+xy²=xy(x+y)=4x7=28.
2:18b（a-b）²-12（b-a）^3
=18b(b-a)²-12(b-a)(b-a)²
=(b-a)²[18b-12(b-a)]
=(b-a)²(12a+6b)
=6(2a+b)(b-a)²
3:x^3-16xy²=x(x²-16y²)=x(x+4y)(x-4y)
4:18a-12ax+2ax²
=2a(x²-6x+9)
=2a(x-3)²
5:x²-5x-24
=(x-8)(x+3)
6:am-2bm-2bm+an
=a(m+n)-4bm
是不是
am-2bm-2bn+an
=a(m+n)-2b(m+n)
=(m+n)(a-2b)
7:（a²+4b²）²-16a²b²
=a^4+16b^4+8a²b²-16a²b²
=a^4+16b^4-8a²b²
=(a²-4b²)²