Question

计算，要有过程

x的4次方-x²=
a（x²-y²）+b（y²-x²）=
-27x的4次方+18x³-3x²=
x的4次方-1=
a的4次方-2a²b²+b的4次方=

Answer 1

x的4次方-x²=x²(x²-1)=x²(x+1)(x-1)

a（x²-y²）+b（y²-x²）=a(x²-y²)-b(x²-y²)=(x²-y²)(a-b)=(x+y)(x-y)(a-b)

-27x的4次方+18x³-3x²=-3x²(9x²-6x+1)=-3x²(3x-1)²

x的4次方-1=(x²+1)(x²-1)=(x²+1)(x+1)(x-1)

a的4次方-2a²b²+b的4次方=(a²-b²)²=(a+b)²(a-b)²