因式分解练习题(1)-6ax3y+8x2y2-2x2y(2)3a2(x-y)3-4b2(y-x)2(3)(x+y)(m-a)-3y(a-m)2+(a-m)3(4)8x(a-1)-4(1-a)(5)m(1-a)+mn(1-a)+1-a(1)16x4-64y4(2)16x6-1/4(3)(a6+b4)2-4a6b4(5)-2m8+512(6)(x+y)3-64或m3-64n3

Question

因式分解练习题(1)-6ax3y+8x2y2-2x2y (2)3a2(x-y)3-4b2(y-x)2 (3)(x+y)(m-a)-3y(a-m)2+(a-m)3 (4)8x(a-1)-4(1-a) (5)m(1-a)+mn(1-a)+1-a (1)16x4-64y4 (2)16x6-1/4 (3)(a6+b4)2-4a6b4 (5)-2m8+512 (6)(x+y)3-64或m3-64n3

Answer 1

(1)-6ax^3y+8x^2y^2-2x^2y =2x^2y(-3ax+4y-1) (2)3a^2(x-y)^3-4b^2(y-x)^2 =(x-y)^2(3a^2-4b^2) =(x-y)^2(3^0.5a+2b)(3^0.5a-2b) (3)(x+y)(m-a)-3y(a-m)^2+(a-m)^3 =(a-m)[(a-m)^2-3y(a-m)-(x-y)] 此题是不是有错,按照道理后面这一项还可以再分解的,是关于(a-m)的分解式 (4)8x(a-1)-4(1-a) =4(a-1)(2x+1) (5)m(1-a)+mn(1-a)+1-a =(1-a)(m+mn+1) 此题是不是有错,按照道理后面这一项还可以再分解的 例如:m+n+mn+1=(m+1)(n+1) (1)16x4-64y4 =16(x^4-4y^4) =16(x^2+2y^2)(x-2^0.5y)(x+2^0.5y) (2)16x6-1/4 =1/4(64x^6-1) =1/4(8x^3-1)(8x^3+1) =1/4(2x-1)(4x^2+2x+1)(2x+1)(4x^2-2x+1) (3)(a6+b4)2-4a6b4 =a^12+2a^6b^4+b^8-4a^6b^4 =a^12-2a^6b^4+b^8 =(a^6-b^4)^2 =(a^3+b^2)^2(a^3-b^2)^2 (5)-2m8+512 =-2(m^8-256) =-2(m^4-16)(m^4+16) =-2(m^2-4)(m^2+4)(m^4+16) =-2(m-2)(m+2)(m^2+4)(m^4+16) (6)(x+y)3-64 =(x+y-4)(x^2+2xy+y^2+4x+4y+16) 或m3-64n3 =(m-4n)(m^2+4mn+16n^2)