因式分解 81(x+y)的四次方减去16(x-y)的四次方

81(x+y)的四次方减去16(x-y)的四次方 要过程,谢谢
2025-12-15 02:47:52
推荐回答(2个)
回答1:

平方差公式,81(x+y)^4-16(x-y)^4=[9(x+y)^2+4(x-y)^2]*[9(x+y)^2-4(x-y)^2]=……

回答2:

81(x+y)^4-16(x-y)^4
=[9(x+y)^2+4(x-y)^2][9(x+y)^2-4(x-y)^2]]
=[9(x+y)^2+4(x-y)^2][3(x+y)+2(x-y)][3(x+y)-2(x-y)]
=(13x^2+10xy+13y^2)(5x+y)(x+5y)