初二数学真题临摹
解:原公式=(1+y)2+2(1+y)x2(1-y)+x4(1-y)2-2(1+y)。
=[(1+y)+x2(1-y)]2-2(1+y)x2(1-y)-2x 2(1+y)
=[(1+y)+x^2(1-y)]^2-(2x)^2
=[(1+y)+x^2(1-y)+2x][(1+y)+x^2(1-y)-2x]
=(x^2-x^2y+2x+y+1)(x^2-x^2y-2x+y+1)
=[(x+1)^2-y(x^2-1)][(x-1)^2-y(x^2-1)]
=(x+1)(x+1-xy+y)(x-1)(x-1-xy-y)。
2.验证:对于任意实数x，y，下面公式的值不会是33:
x^5+3x^4y-5x^3y^2-15x^2y^3+4xy^4+12y^5.
解:原公式=(x ^ 5+3x ^ 4y)-(5x ^ 3y ^ 2+15x ^ 2y ^ 3)+(4xy ^ 4+12y ^ 5)
=x^4(x+3y)-5x^2y^2(x+3y)+4y^4(x+3y)
=(x+3y)(x^4-5x^2y^2+4y^4)
=(x+3y)(x^2-4y^2)(x^2-y^2)(1)(-2x？y？)?。(xy)？(xy)？=4x^8 y^10
(2)(2a+3b)(2a-b)=4a？-2ab+6ab-3b？=4a？+4ab-3b？
(3)5x？(x+1)(x-1)=5x？(x？-1)=5x^4 -5x？
(4)(2x+y-1)？=(2x+y)？-2(2x+y)+1= 4x？+4xy+y？-4x-2y+1
(5)59.8×60.2=(60-0.2)*(60+0.2)=60?-0.2?=3600-0.04= 3599.96
(6)198?=(200-2) ?=200?-2*2*200+2?=40000-800+4=39204
(7)(2a) b^4=4a？b^4
(8) (-2/3 a^7b^5)÷3/2a？b^5= (-2* a^7 b^5* 2a？B 5)/(3 * 3)-A 7 B 5不是分母吧？
= -4/9( a^9 b^10)
=(-2 * 2a？B 5)/(3 A 7 B 5 * 3) =-4/(9 A 5)-A 7 B 5作为分母。
(9)(6/5 a？x^4-0.9ax？)÷3/5ax？=2a？x - 1.5
(10)(7x？y？-8x？y？z)÷8x？y？=(7/8) y - xz
(11)12^13÷(3^10?4^11)=(3*4)^13÷(3^10?4^11)=34?=27?16=432
(12)(因式分解问题)
1.25x？-16y？=(5x)？- (4y)？=(5x-4y)(5x+4y)-平方差
2.(a-b)(x-y)-(b-a)(x+y)=(a-b)[(x-y)+(x+y)]= 2x(a-b)
3.a？-4ab+4b？=a？- 2?答？2b+(2b)？=(a-2b)？
4.4+12(x-y)+9(x-y)？=2?+ 2*2*3(x-y) +9(x-y)？=[2+3(x-y)]？=(3x-3y+2)？
希望你能采用1.xn+4-169xn+2 (n为自然数)；
解决方案:xn+4-169xn+2。
=xn+2(x2-169)
= xn+2(x+13)(x-13)；
2.(a+2b)2-10(a+2b)+25；
解法:(a+2b) 2-10 (a+2b)+25
=(a+2 B- 5)2；
3.2 xy+9-x2-y2；
解决方案:2xy+9-x2-y2
=9-x2+2xy-y2
=9-(x2-2xy+y2)
=32-(x-y)2
=(3+x-y)(3-x+y)；
=(x+3y)(x+y)(x-y)(x+2y)(x-2y)。x^4-2x^3-35x^2 x^8-y^8 25(x-2y)^2-4(2y-x)^2
x^2-4xy+4y^2-9 x^5-1-a(a-x)(x-b)+ab(b-x)(a-x)
ax^2-bx^2-bx+ax+b-a(x+1)(x+2)(x+3)(x+4)-24
(x+y)^2-3(x+y)+2 x^2-7x-①:x^2(a-b)+(b-a)
②:x^2y-2xy^2+y^3
③:(b-a)^2+2(a-b)+1
④:(x^2-y^2)^2-(x^2+y^2)^2
⑤:xy^3-6x^2y^2+xy^3
⑥:(3a-b)^2-(b-3a)^2
⑦:x^2(a+b)-36(b+a)
⑧:36b-a^2b
⑨:(a-b)^2+2(b-a)+49
⑩: x^2-4xy+4y^2-9 10