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Câu a : ( Mình nghĩ đề sai )
Câu b : \(x^3-3x^2+3x-1=\left(x-1\right)^3=\left(x-1\right)\left(x-1\right)\left(x-1\right)\)
Câu c : \(\dfrac{1}{27}+x^3=\left(\dfrac{1}{3}\right)^3+x^3=\left(\dfrac{1}{3}+x\right)\left(\dfrac{1}{9}-\dfrac{1}{3}x+x^2\right)\)
Câu d : \(0,001-1000x^3=\left(\dfrac{1}{10}\right)^3-\left(10x\right)^3=\left(\dfrac{1}{10}-10x\right)\left(\dfrac{1}{100}+x+100x^2\right)\)
Chúc bạn học tốt
a: Sửa đề: \(27x^3-27x^2+9x-1\)
\(=\left(3x-1\right)^3\)
b: \(=\left(x-1\right)^3\)
c: \(=\left(x+\dfrac{1}{3}\right)\left(x^2-\dfrac{1}{3}x+\dfrac{1}{9}\right)\)
Câu a : \(1,24^3-0,24^3=\left(1,24-0,24\right)\left(1,24^2+1,24.0,24+0,24^2\right)=1.\left(1,5376+0,2976+0,0576\right)\)
Câu b : \(\left(a-1\right)^3+\left(a+1\right)^3=\left(a-1+a+1\right)\left[\left(a-1\right)^2-\left(a-1\right)\left(a+1\right)+\left(a+1\right)^2\right]=2a\left(a^2+3\right)\)
Câu c : \(a^6-b^6=\left(a^3\right)^2-\left(b^3\right)^2=\left(a^3-b^3\right)\left(a^3+b^3\right)=\left(a-b\right)\left(a+b\right)\left(a^2-ab+b^2\right)\left(a^2+ab+b^2\right)\)
Chúc bạn học tốt
\(\left(a-1\right)^3-\left(a+1\right)^3=a^3-3a^2+3a-1-a^3-3a^2-3a-1=-6a^2-2=-2\left(3a^2+1\right)\)
Câu a : \(x^3y^3+225=\left(xy\right)^3+\left(\sqrt[3]{225}\right)^3=\left(xy+\sqrt[3]{225}\right)\left(x^2y^2-xy\sqrt[3]{225}+\left(\sqrt[3]{225}\right)^2\right)\)
Chúc bạn học tốt
\(x^3y^3+255=\left(xy+\sqrt[3]{225}\right)\left(x^2y^2-xy\sqrt[3]{225}+\sqrt[3]{225^2}\right)\)
a)\(3x\left(x^2-2x\right)\)
\(=3x^3-6x^2\)
b) \(\left(27x^3-1\right):\left(9x^2+3x+1\right)\)
\(=\left(3x-1\right)\left(9x^2+3x+1\right):\left(9x^2+3x+1\right)\)
\(=3x-1\)
c) \(\dfrac{4y^3}{7x^2}.\dfrac{14x^3}{y}\)
\(=8xy^2\)
\(\)d)\(\dfrac{x^2-9}{2x+6}:\dfrac{3-x}{2}\)
\(=-\dfrac{\left(x-3\right)\left(x+3\right)}{2\left(x+3\right)}:\dfrac{x-3}{2}\)
\(=-\dfrac{\left(x+3\right)\left(x-3\right)}{2\left(x+3\right)}.\dfrac{2}{\left(x-3\right)}\)
\(=-1\)
a.3x(x2-2x)=3x3-6x2
b.(27x3-1) : (9x2+3x+1)=\([\left(3x\right)^3-1]:\left(9x^2+3x+1\right)=\left(3x-1\right)\left(9x^2+3x+1\right):\left(9x^2+3x+1\right)=3x-1\)
\(\left(a-1\right)^3-\left(a+1\right)^3\)
\(=\left[\left(a-1\right)-\left(a+1\right)\right]\left[\left(a-1\right)^2+\left(a-1\right)\left(a+1\right)+\left(a+1\right)^2\right]\)
\(=\left(-2\right)\left(a^2-2a+1+a^2-1+a^2+2a+1\right)\)
\(=\left(-2\right)\left(3a^2+1\right)\)