Question

因式分解的数学题

1、（a+3) (a-7)+25
2、3x^6 - 3x^2
3、25(x-2y)^2-4(2y-x)^2
4、x^4-18x^2+81
5、已知2x-y=1/3,xy=2,求2x^4y^3 - x^3y^4
6、若x、y互为相反数，且(x+2)^2-(y+1)^2=4,求x、y的值
7、已知a+b=2，求(a^2-b^2)^2-8(a^2+b^2)的值
8、（a-2)(a^2+a+1)+(a^2-1)(2-a),其中a=18
9、化简与求值：(a+b)(a-b)+(a+b)^2-a(2a+b),其中a=1/3,b=-1/1/2
过程要全，步骤要写清楚，谢谢啦！（不要只写答案）

Answer 1

1、（a+3) (a-7)+25
=a平方-4a-21+25
=a平方-4a+4
=(a-2)平方
2、3x^6 - 3x^2
=3x^2(x^4-1)
=3x^2(x^2+1)(x^2-1)
=3x^2(x^2+1)(x+1)(x-1)

3、25(x-2y)^2-4(2y-x)^2
=[5(x-2y)-2(2y-x)][5(x-2y)+2(2y-x)]
=(7x-14y)(3x-6y)
=21(x-2y)(x-2y)
=21(x-2y)^2
4、x^4-18x^2+81
=(x^2-9)^2
=(x-3)^2(x+3)^2
5、已知2x-y=1/3,xy=2,求2x^4y^3 - x^3y^4
2x^4y^3 - x^3y^4
=x^3y^3(2x-y)
=(xy)^3(2x-y)
=2^3*(1/3)
=8/3
6、若x、y互为相反数，且(x+2)^2-(y+1)^2=4,求x、y的值
x、y互为相反数
则y=-x
则(x+2)^2-(y+1)^2=4
为(x+2)^2-(-x+1)^2=4
x^2+4x+4-(x^2-2x+1)=4
6x=1
x=1/6
则y=-1/6
7、已知a+b=2，求(a^2-b^2)^2-8(a^2+b^2)的值
(a^2-b^2)^2-8(a^2+b^2)
=(a+b)^2(a-b)^2-8(a^2+b^2)
=4(a-b)^2-8(a^2+b^2)
=4(a^2-2ab+b^2)-8(a^2+b^2)
=4a^2-8ab+4b^2-8a^2-8b^2
=-4(a^2+2ab+b^2)
=-4(a+b)^2
=-4*2^2
=-16
8、（a-2)(a^2+a+1)+(a^2-1)(2-a),其中a=18
（a-2)(a^2+a+1)+(a^2-1)(2-a)
=（a-2)[(a^2+a+1)-(a^2-1)]
=a(a-2)
a=18
a(a-2)
=18*(18-2)
=288
9、化简与求值：(a+b)(a-b)+(a+b)^2-a(2a+b),其中a=1/3,b=-1/1/2
(a+b)(a-b)+(a+b)^2-a(2a+b)
=(a+b)[(a-b)+(a+b)]-a(2a+b)
=2a(a+b)-a(2a+b)
=a(2a+2b-2a+b)
=3ab
a=1/3,b=-1/1/2
3ab
=3*(1/3)*(-1/1/2)
=-1/1/2

Answer 2

(a+3)(a-7)+25
=a平方-4a-21+25
=a平方-4a+4
=(a-2)平方
2、3x^6 - 3x^2
=3x^2(x^4-1)
=3x^2(x^2+1)(x^2-1)
=3x^2(x^2+1)(x+1)(x-1)

25(x-2y)^2-4(2y-x)^2
=[5(x-2y)-2(2y-x)][5(x-2y)+2(2y-x)]
=(7x-14y)(3x-6y)
=21(x-2y)(x-2y)
=21(x-2y)^2
x^4-18x^2+81
=(x^2-9)^2
=(x-3)^2(x+3)^2
已知2x-y=1/3,xy=2,求2x^4y^3 - x^3y^4
2x^4y^3 - x^3y^4
=x^3y^3(2x-y)
=(xy)^3(2x-y)
=2^3*(1/3)
=8/3
若x、y互为相反数，且(x+2)^2-(y+1)^2=4,求x、y的值
x、y互为相反数
则y=-x
则(x+2)^2-(y+1)^2=4
为(x+2)^2-(-x+1)^2=4
x^2+4x+4-(x^2-2x+1)=4
6x=1
x=1/6
则y=-1/6
7、已知a+b=2，求(a^2-b^2)^2-8(a^2+b^2)的值
(a^2-b^2)^2-8(a^2+b^2)
=(a+b)^2(a-b)^2-8(a^2+b^2)
=4(a-b)^2-8(a^2+b^2)
=4(a^2-2ab+b^2)-8(a^2+b^2)
=4a^2-8ab+4b^2-8a^2-8b^2
=-4(a^2+2ab+b^2)
=-4(a+b)^2
=-4*2^2
=-16
8、(a-2)(a^2+a+1)+(a^2-1)(2-a),其中a=18
(a-2)(a^2+a+1)+(a^2-1)(2-a)
=(a-2)[(a^2+a+1)-(a^2-1)]
=a(a-2)
a=18
a(a-2)
=18*(18-2)
=288
9、化简与求值:(a+b)(a-b)+(a+b)^2-a(2a+b),其中a=1/3,b=-1/1/2
(a+b)(a-b)+(a+b)^2-a(2a+b)
=(a+b)[(a-b)+(a+b)]-a(2a+b)
=2a(a+b)-a(2a+b)
=a(2a+2b-2a+b)
=3ab