初一数学,乘法公式的

1.a^4+b^4+c^4+d^4-4abcd
=(a^4+b^4-2a^2b^2)+(c^4+d^4-2c^2d^2)+2(a^2b^2-2abcd+c^2d^2)
=(a^2-b^2)^2+(c^2-d^2)^2+(ab-cd)^2
=0
所以
a^2-b^2=0,c^2-d^2=0,ab-cd=0
所以，a=b=c=d(a,b,c,d为正数时）
反例：a=b=1,c=d=-1

2.a(a+1)(a+2)(a+3)+1
=a(a+3)(a+1)(a+2)+1
=(a^2+3a)(a^2+3a+2)+1
=(a^2+3a)^2+2(a^2+3a)+1
=(a^2+3a+1)^2

3.
因为十位数字相同
所以，设这两个数为：x,x+2
(x+2)^2-x^2=220
4x+4=220
x=54
x+2=56
这两个数为:54,56

4. (1)(a-b-c+d)(a+b-c-d)
=(a-c)^2-(b-d)^2
=a^2+c^2-2ac-b^2-d^2+2bd

(2) (x+2y-z)(x-2y+z)-(x+2y+z)^2
=x^2-(2y-z)^2-(x+2y+z)^2
=x^2-4y^2-z^2+4yz-x^2-4y^2-z^2-4xy-4yz-2xz
=-8y^2-2z^2-4xy-2xz

1. a^4+b^4+c^4+d^4 -2a^2b^2-2c^2d^2 + 2a^2b^2+2c^2d^2-4abcd=0
(a^2-b^2)^2 +(c^2 -d^2)^2 +2(ab-cd)^2 =0
a=b,c=d,ab=cd
所以：a=b=c=d

2, x-1,x,x+1,x+2
(x-1)x(x+1)(x+2)+1 = x^4 +2x^3-x^2-2x+1 = (x^2+x-1)^2

3.设十位为a，(10a+6)^2 -(10a+4)^2 = 220, a=5

4.1) = ((a-c)-(b-d))((a-c)+(b-d))=(a-c)^2 - (b-d)^2
= a^2-b^2+c^2-d^2 -2a^2c^2 +2b^2d^2

2)同理 = (x+（2y-z))(x-(2y-z))-(x+(2y+z))^2
= x^2 - (2y-z)^2 -x^2-(2y+z)^2-2x(2y+z)
= -8y^2-2z^2-4xy-2xz