Question

2a^3-8a^2+8a 分解因式

（1）2a^3-8a^2+8a
（2）a^3-4AB^2
(3)2a(x^2+1)^2-8ax^2

Answer 1

解
2a³-8a²+8a
=2a(a²-4a+4)
=2a(a-2)²

a³-4ab²
=a(a²-4b²)
=a(a-2b)(a+2b)

2a(x²+1)²-8ax²
=2a[(x²+1)²-4x²]
=2a[(x²+1)+2x][(x²+1)-2x]
=2a(x+1)²(x-1)²

Answer 2

（1）2a(a+2)^2
(2)a(a+2b)(a-2b)
(3)=2a[(x^2+1)^2-4x^2]
=2a[(x^2+1+2x)(x^2+1-2x)]
=2a[(x+1)^2-(x-1)^2