题目

求解：27x^3+54x^2y+36xy^2+8y^3= 还有下面的,要完整过程哦
a^2-c^2+2ab+b^2-d^2-2cd=
x^4+2x^2+1-x^2-2ax-a^2=
都是因式分解,我不太懂,希望高手教下,谢谢!
(x+y)^2+(x+m)^2-(m+n)^2-(y+n)^2=
25x^2-4a^2+12ab-9b^2=
a^2-4b^2-4c^2-8bc=

提问时间：2020-11-03

答案

27x^3+54x^2y+36xy^2+8y^3
=(3x+2y)³
根据公式:(a+b)³=a³+3a²b+3ab²+b³
a^2-c^2+2ab+b^2-d^2-2cd
=a^2+2ab+b^2-(c^2+2cd+d^2)
=(a+b)^2-(c+d)^2
=(a+b+c+d)(a+b-c-d)
x^4+2x^2+1-x^2a-2ax-a^2
=(x²+1)^2-(x+a)%2
=(x²+x+a+1)(x²-x-a+1)
(x+y)^2-(m+n)^2+(x+m)^2-(y+n)^2
=(x+y+m+n)(x+y-m-n)+(x+y+m+n)(x+m-y-n)
=(x+y+m+n)(x+y-m-n+x+m-y-n)
=2(x+y+m+n)(x-n)
25x^2-4a^2+12ab-9b^2
=25x^2-(2a-3b)^2
=（5x+2a-3b）（5x-2a+3b）
a^2-4b^2-4c^2-8bc
=a^2-4(b+c)^2
=(a+2b+2c)(a-2b-2c)