Question

运用整式乘法公式 0.345^2 +1.345^2-0.345*2.69 。计算：(y-x)^3*(x-y)^m-(x-y)^m+2*(y-x)

Answer 1

（1）(x-a)²=x²-2ax+a²,此时等于代数式x²-8x+2b
可知-2a=-8,a=4;a²=16=2b,b=8
因此b-ab=8-32=-24
(2)用一个边长为a的正方形和四个长方形得到的面积为a²+4ab,需要再用边长为b的正方形拼成大正方形，即a²+4ab+_b²=( )²,显然根据代数式前两项可得(a+2b)²=a²+4ab+4b²
因此需要4个边长为b的正方形，拼成一个边长为a+2b的大正方形

①x^2-8x+2b=(x-a)^2=x^2-2ax+a^2,对应系数相等，则8=2a,2b=a^2,所以a=4,b=8,则b-ab=-24.

Answer 2

0.345^2 +1.345^2-0.345*2.69
=0.345^2 +1.345^2-2*0.345*1.345
=(0.345-1.345)^2
=(-1)^2
=1

(y-x)^3*(x-y)^m-(x-y)^(m+2)*(y-x)
=- (x-y)^3*(x-y)^m+(x-y)^(m+2)*(x-y)
=- (x-y)^(3+m)+(x-y)^(m+2+1)
=- (x-y)^(3+m)+(x-y)^(m+3)
=0

Answer 3

0.345^2 +1.345^2-0.345*2.69
=0.345^2-2*0.345*1.345+1.345^2
=(1.345-0.345)^2
=1
(y-x)^3*(x-y)^m-(x-y)^m+2*(y-x)
=-(x-y)^3(x-y)^m-(x-y)^m-2(x-y)
=-(x-y)[(x-y)^(m+2)+(x-y)^(m-1)+2]

Answer 4

0.345^2 +1.345^2-0.345*2.69
=0.345^2 +1.345^2-2*0.345*1.345
=(0.345-1.345)^2
=(-1)^2
=1

(y-x)^3*(x-y)^m-(x-y)^(m+2)*(y-x)
=0