Question

分解下列因式

x4次方+4分之81 x4次方+x2次y2次+y4 次 x2次y-7xy+6y

Answer 1

X4+81/4=(x2)2+(9/2)2=（x2+9/2）2-2x2*9/2=（x2+9/2）2-9x2=（x2+9/2）2-(3x)2= (x2+9/2+3x)*( x2+9/2-3x)
X4+x2y2+y4=(x2+y2)2- x2y2=( x2+y2+xy)*( x2+y2-xy)=((x+y)2-xy)*((x-y)2+xy)

Answer 2

x^4-81/4=(x²+9/2)(x²-9/2)
x^4+2x²y²+y^4=(x²+y²)²
x²y-7xy+6y=y(x²-7x+6)=y(x-1)(x-6)