一、计算题 1、(-2(x-y)^2)^2 * (y-x)^3 2、(9⼀4 * 10^2) * (25 * 10^3)^2 * (-2 * 10^10)^2

一、计算题
1、(-2(x-y)^2)^2 * (y-x)^3=4*(x-y)^4*[-(x-y)^3]=-4*(x-y)^7
2、(9/4 * 10^2) * (25 * 10^3)^2 * (-2 * 10^10)^2=9/4 * 10^2* 25 ^2*10^6* 4*10^20=75^2*10^28
3、(2a^2 b^3)^3 * (-3a^2 b)^2 * 1/72abc=2^6*a^6*b^9*6^2*a^4*b^2*1/72*abc=2^5*a^11*6^10*c
4、(2x+3y)(3x-5y)-(x+y)(6x-7y)=6x^2-10xy+9xy-15y^2-6x^2+7xy-6xy+7y^2=-8y^2
5、(x-1)(x+1)(x^2+1) - (x^2+1)(x^2-2) 其中x=1/2
=(x^2-1)(x^2+1)-(x^2+1)(x^2-1-1)=x^4-1-(x^4-1)+x^2+1=x^2+1=5/4
6、(2a+b)(2a-b)+3(2a-b)^2+(-3a)(4a-3b) 其中a=-1 b=2
=4a^2-b^2+3(4a^2-4ab+b^2)-12a^2+9ab=4a^2-3ab+2b^2=18
二、解方程
7、x^2(2x^2-3x-1)+x^3(x-2)=3x(x^3-2x^2-1/3x-1)+x^3+6
2x^4-3x^3-x^2+x^4-2x^3=3x^4-6x^3-x^2-3x+x^3+6
0=-3x+6
x=2
8、 (2x+3)(x-4)=(x-2)(2x+5)
2x^2-8x+3x-12=2x^2+5x-4x-10
-6x=2
x=-1/3
9、 3^x+1 * 5^x+1=15^2x-3
15^2x+3^x+5^x+1=15^2x-3
3^x+5^x=(15^-3)-1
{没看懂这道题，貌似无解，不晓得是不是我解错了}
三、解答题
10、若n为自然数，试说明整式m(2n+1)-2n(n-1)的值一定是3的倍数
{是不是输错了哦，m该是n吧}
解： n(2n+1)-2n(n-1)=2n^2+n-2n^2+2n=3n
∵n为自然数
∴3n一定是3的倍数
11、已知x+y=10 x * y=18.75 求 1、x^2+y^2 2、(x-y)^2的值
解：1、x^2+y^2=x^2+y^2+2x * y-2x * y=（x+y）^2-2x * y=10^2-2*18.75=62.5
2、(x-y)^2=x^2-2x * y+y^2=（x+y）^2-4x * y=10^2-4*18.75=25
12、当k取哪些整数时，关于x的多项式x^2+kx+6可以用十字相乘法进行因式分解？请逐一举出这样的整数k的值，及当时因式分解的结果。
解：∵k取整数
∴6可以分解为1*6，2*3
故，k可取7和5
k=7时，x^2+7x+6=(x+1)(x+6)
k=5时，x^2+5x+6=(x+2)(x+3)
13、长方形的长为a米，宽为b米，a＞b，若将长增加1米，宽减少1.5米，问此时长方形的面积是增加了还是减少了？增加或减少了多少平方米？
解：设原长方形的面积为S1，变化后的面积为S2
则，S1=ab
S2=(a+1)(b-1.5)=ab-1.5a+b-1.5
S1-S2=1.5a-b+1.5
∵a＞b
∴1.5a-b+1.5>0
故，此时的长方形面积增加了，增加（1.5a-b+1.5）平方米
14、若p、q、a均为整数，且p＞q, (x+p)(x+q)=x^2-ax-8,求所有可能的a的值及对应的p、q的值
解：
∵ p、q、a均为整数，(x+p)(x+q)=x^2-ax-8
∴-8可以分解为-1*8，1*-8，-2*4，2*-4
故，a可取7，-7，2，-2
又∵p＞q
∴a=7时，p=8，q=-1
a=-7时，p=1，q=-8
a=2时，p=4，q=-2
a=-2时，p=2，q=-4

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