因式分解(1)a²x²+4ax²y+4x²y²;(2)x³+
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/22 09:18:31
因式分解(1)a²x²+4ax²y+4x²y²;(2)x³+2x+3;(3)a²b-6ab²+9b³;(4)a³-2a²+a;(5)ax²-10ax+25a;(6)已知a+5=-5,ab=7.求(a-b)²的值补充:(3)、(4)、(5)可以直接出答案,剩下的3道题均要完成过程.
解
a²x²+4ax²y+4x²y²
=x²(a²+4ay+4y²)
=x²(a+2y)²
x³+2x+3
=(x³+1)+(2x+2)
=(x+1)(x²-x+1)+2(x+1)
=(x+1)(x²-x+1+2)
=(x+1)(x²-x+3)
原式
=b(a²-6ab+9b²)
=b(a-3b)²
原式
=a(a²-2a+1)
=a(a-1)²
原式
=a(x²-10x+25)
=a(x-5)²
(a-b)²
=(a²-2ab+b²)
=(a²+2ab+b²)-4ab
=(a+b)²-4ab
=(-5)²-4×7
=25-28
=-3
a²x²+4ax²y+4x²y²
=x²(a²+4ay+4y²)
=x²(a+2y)²
x³+2x+3
=(x³+1)+(2x+2)
=(x+1)(x²-x+1)+2(x+1)
=(x+1)(x²-x+1+2)
=(x+1)(x²-x+3)
原式
=b(a²-6ab+9b²)
=b(a-3b)²
原式
=a(a²-2a+1)
=a(a-1)²
原式
=a(x²-10x+25)
=a(x-5)²
(a-b)²
=(a²-2ab+b²)
=(a²+2ab+b²)-4ab
=(a+b)²-4ab
=(-5)²-4×7
=25-28
=-3
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