因式分解问题(x+2y)²-4z²

题目

因式分解问题(x+2y)²-4z²
(x+2y)²-4z²
a²（a-b）+b²（b-a）
-196a²b²+81x4次方y²
4（x+2y）²-25（x-2y)²
4(x+y+z)²-9(x-y-z)²
急等着用

答案

解
(x+2y)²-4z²
=(x+2y)²-(2z)²
=(x+2y-2z)(x+2y+2z)
a²(a-b)+b²(b-a)
=a²(a-b)-b²(a-b)
=(a-b)(a²-b²)
=(a-b)(a-b)(a+b)
=(a-b)²(a+b)
-196a²b²+81x^4y²
=(9x²y)²-(14ab)²
=(9x²y-14ab)(9x²y+14ab)
4(x+2y)²-25(x-2y)²
=[2(x+2y)]²-[5(x-2y)]²
=[2(x+2y)-5(x-2y)][2(x+2y)+5(x-2y)]
=(14y-3x)(7x-6y)
4(x+y+z)²-9(x-y-z)²
=[2(x+y+z)]²-[3(x-y-z)]²
=[2(x+y+z)-3(x-y-z)][2(x+y+z)+3(x-y-z)]
=(5y-x+5z)(5x-y-z)