Question

求（x-2y）²-4（2x-y）²=？16（x+y)²-25（x-y)²=？a的2n+1次方-16a的2n-1次方

Answer 1

（x-2y）²-4（2x-y）²
=(x-2y+2(2x-y))(x-2y-2(2x-y))
=(5x-4y)(-3x)
=-3x(5x-4y)
16（x+y)²-25（x-y)²
=(4(x+y)+5(x-y))(4(x+y)-5(x-y))
=(9x-y)(-x+9y)
a的2n+1次方-16a的2n-1次方
=a^(2n-1)(a^2-16)
=a^(2n-1)(a+4)(a-4)

Answer 2

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

16（x+y)²-25（x-y)²
=[4(x+y)-5(x-y)][4(x+y)+5(x-y)]
=(4x+4y-5x+5y)(4x+4y+5x-5y)
=(9y-x)(9x-y)

a的2n+1次方-16a的2n-1次方
=a的2n-1次方(a²-16)
=a的2n-1次方(a-4)(a+4)