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\(a^{10}+a^5+1\)
\(=\left(a^{10}-a\right)+\left(a^5-a^2\right)+\left(a^2+a+1\right)\)
\(=a\left(a^3-1\right).\left(a^6+a^3+1\right)+a^2\left(a^3-1\right)+\left(a^2+a+1\right)\)
\(=a\left(a-1\right)\left(a^2+a+1\right)+\left(a^6+a^3+1\right)+a^2\left(a-1\right)\left(a^2+a+1\right)\)+ (a²+a+1)
Đến đây rùi thì tự làm tiếp nha
a5+a+1=a5+a4+a3+a2+a+1-a4-a3-a2
=a3.(a2+a+1)+(a2+a+1)-a2.(a2+a+1)
=(a2+a+1)(a3-a2+1)
Ta có : \(a^5+a+1=\left(a^5-a^2\right)+\left(a^2+a+1\right)\)
\(=a^2\left(a^3-1\right)+\left(a^2+a+1\right)\)
\(=a^2\left(a-1\right)\left(a^2+a+1\right)+\left(a^2+a+1\right)\)
\(=\left(a^2+a+1\right)\left(a^3-a^2+1\right)\)
Ta có : \(a^5+a+1\)
\(=\left(a^5-a^2\right)+\left(a^2+a+1\right)\)
\(=a^2\left(a^3-1\right)+\left(a^2+a+1\right)\)
\(=a^2\left(a-1\right)\left(a^2+a+1\right)+\left(a^2+a+1\right)\)
\(=\left(a^2+a+1\right)\left(a^3-a^2+1\right)\)
\(a^5+a+1\)
\(=\left(a^5-a^2\right)+\left(a^2+a+1\right)\)
\(=a^2\left(a^3-1\right)+\left(a^2+a+1\right)\)
\(=a^2\left(a-1\right)\left(a^2+a+1\right)+\left(a^2+a+1\right)\)
\(=\left(a^2+a+1\right)\left(a^3-a^2+1\right)\)
\(a^5+a+1=a^5+a^4+a^3+a^2+a+1-a^4-a^3-a^2\)
\(=a^2\left(a^3-1\right)+\left(a^2+a+1\right)\)
\(=a^2\left(a-1\right)\left(a^2+a+1\right)+\left(a^2+a+1\right)\)
\(=\left(a^2+a+1\right)\left(a^3-a^2+1\right)\)
Bài này có rất nhiều cách để phân tích lắm
Chúc bạn hok tôt
1a) \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
b) \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
\(a,=-\left(x-1\right)^3\left[=\left(1-x\right)^3\right]\\ b,=\left(1-x\right)^3\)
\(a^{10}+a^5+1\)
\(a^{10}+a^5+1=\left(a^2+a+1\right)\left(a^8-a^7+a^5-a^4+a^3-a+1\right)\)
a^5-a^2+(a^2+a+1)
a^2(a^3-1)+(a^2+a+1)
a^2(a-1)(a^2+a+1)+(a^2+a+1)
(a^2+a+1)[a^2(a-1)]
\(a^5+a^3-a^2-1=a^3\left(a^2+1\right)-\left(a^2+1\right)=\left(a^3-1\right)\left(a^2+1\right)\)
\(a^5+a^3-a^2-1=a^3\left(a^2+1\right)-\left(a^2+1\right)=\left(a^3-1\right)\left(a^2+1\right)=\left(a-1\right)\left(a^2+a+1\right)\left(a^2+1\right)\)
\(a^5+a^3-a^2-1\)
\(=a^3\left(a^2+1\right)-\left(a^2+1\right)\)
\(=\left(a^2+1\right)\left(a^3-1\right)\)