因式分解啊啊啊!要过程

题目

因式分解啊啊啊!要过程
1. x²y²＋1－x²－y²＋4xy
2. 2.x²－y²＋2x－4y－3
3. x的4次方＋x²－2ax－a＋1
4. (x＋y)的4次方＋x的4次方＋y的4次方
5. (a＋b＋c) ³ －(a³＋b³＋c³)

答案

1.x²y²＋1－x²－y²＋4xy
= x²y² + 2xy + 1 - (x² - 2xy + y²)
= (xy + 1)² - (x - y)²
= (xy + 1 + x - y)(xy + 1 - x + y)
= (xy + x - y + 1)(xy - x + y + 1)
2.x²－y²＋2x－4y－3
= x² + 2x + 1 - (y² + 4y + 4)
= (x + 1)² - (y + 2)²
= (x + 1 + y + 2)(x + 1 - y - 2)
= (x + y + 3)(x - y - 1)
3.x⁴＋ x² － 2ax － a² ＋ 1
= (x⁴ + 2x² + 1) - (x² + 2ax + a²)
= (x² + 1)² - (x + a)²
= (x² + x + a + 1)(x² - x - a + 1)
4.(x＋y)⁴＋ x⁴＋ y⁴
= (x + y)⁴+ (x + y)(x)
= (x + y)⁴+ x⁴+ y⁴+ 2x²y² - 2x²y²
= (x² + y²)²
5.(a＋b＋c)³ －(a³＋b³＋c³)
=(a + b + c)³ - a³ - (b³ + c³)
=(b + c)[(a+b+c)² + a(a+b+c) + a²] - (b + c)(b² - bc + c²)
= (b + c)[(a+b+c)² + a(a+b+c) + a² - b² + bc - c²]
= (b + c)[3a² + 3ab + 3ac + 3bc]
= 3(b + c)[a(a + b) + c(a + b)]
= 3(b + c)(a + c)(a + b)
= 3(a + b)(a + c)(b + c)
未完.