题目

因式分解8-（1+X）^3
因式分解 （2-y）^3+8y^3
2（5r-2）^3+128
8C^6+8d^6
a^3+4a-b^3-4b
（5y-4）^3-（y-2）^3
速求

提问时间：2020-11-09

答案

8 - (1+x)^3 = 2^3 - (1+x)^3
= (2 -1 -x)[ 2^2 + 2(1+x) + (1+x)^2]
= ( 1-x)(5 + 4x + x^2)
(2-y)^3+8y^3= (2-y)^3 + (2y)^3 = (2-y +2y)[(2-y)^2 - (2-y)*2y + (2y)^2]
= ( 2 + y)(9y^2 -8y + 4)
2（5r-2）^3+128 =2[ (5r -2)^3 + 64] = 2[(5r -2)^3 + 4^3]
= 2(5r -2 + 4)[(5r-2)^2 - (5r-2)*4 + 4^2]
= 2(5r + 2)(5r^2 -40r + 28)
8C^6+8d^6 = 8[(c^2)3 + (d^2)^3] =
= 8(c2 + d^2)(c^4 -c^2d^2 + d^4)
a^3+4a-b^3-4b = (a^3 -b^3) +4(a-b)
= (a-b)(a^2 + ab + b^2) + 4(a-b)
= (a-b)(a^2 + ab + b^2 +4)
（5y-4）^3-（y-2）^3 = (5y-4 -y +2)[ (5y-4)^2 -(5y-4)(y-2)+(y-2)^2]
= (4y -2)(21y^2 -30y+12)
= 2(2y-1)(21y^2 - 30y + 12)