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因式分解(1)(x-2)(x-4)+1(2)ax²-2a²x+a³(3)a²-2ab+b²-1
题目详情
因式分解(1)(x-2)(x-4)+1(2)ax²-2a²x+a³(3)a²-2ab+b²-1
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答案和解析
解
(x-2)(x-4)+1
=x²-6x+8+1
=x²-6x+9
=(x-3)²
ax²-2a²x+a³
=a(x²-2ax+a²)
=a(x-a)²
a²-2ab+b²-1
=(a-b)²-1
=(a-b+1)(a-b-1)
(x-2)(x-4)+1
=x²-6x+8+1
=x²-6x+9
=(x-3)²
ax²-2a²x+a³
=a(x²-2ax+a²)
=a(x-a)²
a²-2ab+b²-1
=(a-b)²-1
=(a-b+1)(a-b-1)
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