已知乘法公式(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)=a^5+b^5,(a-b)(a^4+a^3b
来源:学生作业帮 编辑:搜搜考试网作业帮 分类:数学作业 时间:2024/08/17 02:00:58
已知乘法公式(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)=a^5+b^5,(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)=a^5+b^5
利用
上述公式分解x^8+x^6+x^4+x^2+1
利用
上述公式分解x^8+x^6+x^4+x^2+1
![已知乘法公式(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)=a^5+b^5,(a-b)(a^4+a^3b](/uploads/image/z/17355096-0-6.jpg?t=%E5%B7%B2%E7%9F%A5%E4%B9%98%E6%B3%95%E5%85%AC%E5%BC%8F%EF%BC%88a%2Bb%29%28a%5E4-a%5E3b%2Ba%5E2b%5E2-ab%5E3%2Bb%5E4%29%3Da%5E5%2Bb%5E5%2C%28a-b%29%28a%5E4%2Ba%5E3b)
初看不能分解,但稍做变形即可
(x^8+x^6+x^4+x^2+1)
=(x^2-1)(x^8+x^6+x^4+x^2+1)/(x^2-1)
=(x^10-1)/(x^2-1)
=(x^5+1)(x^5-1)/(x^2-1)
=(x+1)(x^4+x^3-x+1)(x-1)(x^4+x^3+x^2+x+1)/(x^2-1)
=(x^4+x^3-x+1)(x^4+x^3+x^2+x+1)
(x^8+x^6+x^4+x^2+1)
=(x^2-1)(x^8+x^6+x^4+x^2+1)/(x^2-1)
=(x^10-1)/(x^2-1)
=(x^5+1)(x^5-1)/(x^2-1)
=(x+1)(x^4+x^3-x+1)(x-1)(x^4+x^3+x^2+x+1)/(x^2-1)
=(x^4+x^3-x+1)(x^4+x^3+x^2+x+1)
已知a-b=5,ab=-4,求代数式5a^2b(a-b)-3ab(b-a)^2+5ab^2(b-a)的值
已知实数a,b满足ab=-1/5,a+b=4/5,求a^2b+ab^2-a^3b^2-a^2b^3
(a-2b)(a^2-2ab+4b^2)-a(a-5b)(a+3b)
已知3a*a+ab-2b*b=0(a不等于0,b不等于0),求a/b-b/a-(a*a+b*b)/ab的值.
1.(a-b)^2(b-a)^3(a-b)^-4
先化简再求值 (a-2b)(a²+2ab+4b²)-a(a-5b)(a+3b),其中a=-1,b=2
已知a²+b²+2a-4b+5=0,则a²-2ab-3b²/a(a-b)+3ab
(2a+b)(2a-b)-3a(4a-3b)+(4a-b)(2a-b) a=5分之3,b=3分之2
已知多项式A=-3a²-2b,B=4a²+5b,计算2A-B
已知A=5a^3b+2a^4-3a^2b-ab^3,B=6ab^3-8a^3b+3a^4-5b^4,求2(2A+B)-3
已知:a-b=4,ab=3,求多项式(2a+5b-3ab)-(a+6b-ab)-(2ab+2b-2a)的值
已知a-b=5,ab=-1,求代数式(22a+3b-2ab)-(a+4b+ab)-(3ab+2b-2a)的值.