\(Bài\) \(9.\)
\(a.\left(2ax+1\right)\left(3ax-2\right)-\left(ax-2\right)\left(6ax-1\right)=10ax\)
\(Cm.\)
\(Ta\) \(có:VT=\left(2ax+1\right)\left(3ax-2\right)-\left(ax-2\right)\left(6ax+1\right)\)
\(=6a^2x^2-ax-2-6a^2x^2+11ax+2\)
\(=6a^2x^2-6a^2x^2-ax+11ax-2+2\)
\(=10ax.\)
\(Vậy\) \(\left(2ax+1\right)\left(3ax-2\right)-\left(ax-2\right)\left(6ax+1\right)=10ax.\)
\(b.\left(a-1\right)\left(a^6+a^5+a^4+a^3+a^2+a+1\right)=a^7-1\)
\(Cm\)
\(Ta\) \(có:VT=\left(a-1\right)\left(a^6+a^5+a^4+a^3+a^2+a+1\right)\)
\(=a\left(a^6+a^5+a^4+a^3+a^2+a+1\right)-1\left(a^6+a^5+a^4+a^3+a^2+a+1\right)\)
\(=a^7+a^6+a^5+a^4+a^3+a^2+a-a^6-a^5-a^4-a^3-a^2-a-1\)
\(=a^7-1.\)
\(Vậy\) \(\left(a-1\right)\left(a^6+a^5+a^4+a^3+a^2+a+1\right)=a^7-1.\)
\(c.\left(x+1\right)\left(x^6-x^5+x^4-x^3+x^2-x+1\right)=x^7+1\)
\(Cm\)
\(Ta\) \(có:\)\(VT=\left(x-1\right)\left(x^6-x^5+x^4-x^3+x^2-x+1\right)\)
\(=x\left(x^6-x^5+x^4-x^3+x^2-x+1\right)+1\left(x^6-x^5+x^4-x^3+x^2-x+1\right)\)
\(=x^7-x^6+x^5-x^4+x^3-x^2+x+x^6-x^5+x^4-x^3+x^2-x+1\)
\(=x^7+1.\)
\(Vậy\)\(\left(x+1\right)\left(x^6-x^5+x^4-x^3+x^2-x+1\right)=x^7+1.\)
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