Question

因式分解：a的4次方-2a的二次方b的二次方-8b的4次方

还有（x的二次方-3）的二次方+（x的二次方-3）-2[没打错..

Answer 1

a的4次方-2a的二次方b的二次方-8b的4次方
=(a²-4b²)(a²+2b²)
=(a+2b)(a-2b)(a²+2b²)

（x的二次方-3）的二次方+（x的二次方-3）-2
=(x²-3-1)(x²-3+2)
=(x²-4)(x²-1)
=(x+2)(x-2)(x+1)(x-1)

Answer 2

a的4次方-2a²b²-8b的4次方
=(a²)²-2a²b²-(2b²)²-(2b²)²
=(a²+2b²)(a²-2b²)-2b²(a²+2b²)
=(a²+2b²)(a²-2b²-2b²)
=(a²+2b²)(a²-4b²)

（x²-3）²+（x²-3）-2
=(x²-3-1)(x²-3+2)
=(x²-4)(x²-1)
=(x+2)(x-2)(x+1)(x-1)

Answer 3

（1）原式=(a²)²-2a²b²-(2b²)²-(2b²)²
=(a²+2b²)(a²-2b²)-2b²(a²+2b²)
=(a²+2b²)(a²-2b²-2b²)
=(a²+2b²)(a²-4b²)

（2）原式=（x²-3）²+（x²-3）-2
=(x²-3-1)(x²-3+2)
=(x²-4)(x²-1)
=(x+2)(x-2)(x+1)(x-1)

Answer 4

（a的平方-4倍b的平方）*（a的平方+2倍b的平方）
（x的平方-1）*（x的平方-4）