（x-y)^3-(y-x)^25a^2(x-y)+10a(y-x)(m-n)^2-10(n-m)+25(x+y)^2-2(x+y)(x-y)+(x-y)^2x^2+12xy+36y^21-8xy^2+16x^2y^4x^4-8x^2+164（x-y)^2-4(x-y)+118x^3-27x^4-3x^2x^4-18x^2+8116a^2b^4-8ab^2c^2+c^49(2x-y)^2-6(2x-y)+1^几就是几次方

Question

（x-y)^3-(y-x)^2
5a^2(x-y)+10a(y-x)
(m-n)^2-10(n-m)+25
(x+y)^2 -2(x+y)(x-y)+(x-y)^2
x^2 +12xy+36y^2
1-8xy^2+16x^2y^4
x^4-8x^2+16
4（x-y)^2-4(x-y)+1
18x^3-27x^4-3x^2
x^4-18x^2+81
16a^2b^4-8ab^2c^2+c^4
9(2x-y)^2-6(2x-y)+1
^几就是几次方

Answer 1

(1)
(x-y)^3-(y-x)^2
=(x-y)^3-(x-y)^2 (提出公因子(x-y)^2)
=(x-y)^2*(x-y-1)
(2)
5a^2(x-y)+10a(y-x)
=5a^2(x-y)-10a(x-y) (提出公因子5a(x-y))
=5a(x-y)(a-2)
(3)
(m-n)^2-10(n-m)+25
=(m-n)^2+10(m-n)+25 (完全平方公式)
=(m-n+5)^2
(4)
(x+y)^2 -2(x+y)(x-y)+(x-y)^2 (完全平方公式)
=[(x+y)-(x-y)]^2
=(2y)^2
=4y^2
(5)
x^2 +12xy+36y^2
=x^2+2x(6y)+(6y)^2 (完全平方公式)
=(x+6y)^2
(6)
1-8xy^2+16x^2y^4
=1-2*(4x)*y^2+(4x)^2*(y^2)^2 (完全平方公式)
=(1-4xy^2)^2
(7)
x^4-8x^2+16 (完全平方公式)
=(x^2-4)^2 (再由平方差公式)
=[(x+2)(x-2)]^2
=(x+2)^2*(x-2)^2
(8)
4(x-y)^2-4(x-y)+1
=[2(x-y)]^2-2*2(x-y)+1 (完全平方公式)
=[2(x-y)-1]^2
=(2x-2y-1)^2
(9)
18x^3-27x^4-3x^2 (先提出公因子3x^2)
=3x^2(6x-9x^2-1)
=-3x^2(9x^2-6x+1) (括号内为完全平方)
=-3x^2(3x-1)^2
(10)
x^4-18x^2+81 (完全平方公式)
=(x^2-9)^2 (再由平方差公式)
=[(x+3)(x-3)]^2
=(x+3)^2*(x-3)^2
(11)
16a^2b^4-8ab^2c^2+c^4
=(4ab^2)^2-2*(4ab^2)c^2+(c^2)^2 (完全平方公式)
=(4ab^2-c^2)^2
(12)
9(2x-y)^2-6(2x-y)+1
=[3(2x-y)]^2-6(2x-y)+1 (完全平方公式)
=[3(2x-y)-1]^2
=(6x-3y-1)^2