Question

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

Answer 1

(x+2y)²-4z²
=[(x+2y)+2z]*[(x+2y)-2z]
=(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+81x4次方y²
=81x4次方y²-196a²b²
=(9x²+14ab)(9x²-14ab)

4（x+2y）²-25（x-2y)²
=[2（x+2y）+5（x-2y)]*[2（x+2y）-5（x-2y)]
=(7x-6y)(-3x+12y)

4(x+y+z)²-9(x-y-z)²
=[2(x+y+z)+3(x-y-z)]*[2(x+y+z)-3(x-y-z)]
=(5x-y-z)(-x+5y+5z)

Answer 2

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)