viet cac bieu thuc sau duoi dang tich:
a,1,24\(^3\)-0,24\(^3\)
b,(a-1)\(^3\)+(a+1)\(^3\)
c, a\(^6\)-b\(^6\)
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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
\(\left(a-1\right)^3-\left(a+1\right)^3=a^3-3a^2+3a-1-a^3-3a^2-3a-1=-6a^2-2=-2\left(3a^2+1\right)\)
\(a,\left(4-xy\right)^3\)
\(=4^3-3.4^2xy+3.4.x^2y^2-x^3y^3\)
\(=64-48xy+12x^2y^2-x^3y^3\)
\(b,\left(0,1+xy\right)^3\)
\(=\left(0,1\right)^3+3.\left(0,1\right)^2xy+3.0,1.\left(xy\right)^2+x^3y^3\)
\(=0,001+0,03xy+0,3x^2y^2+x^3y^3\)
\(\left(a-1\right)^3-\left(a+1\right)^3\)
\(=\left[\left(a-1\right)-\left(a+1\right)\right]\left[\left(a-1\right)^2+\left(a-1\right)\left(a+1\right)+\left(a+1\right)^2\right]\)
\(=\left(-2\right)\left(a^2-2a+1+a^2-1+a^2+2a+1\right)\)
\(=\left(-2\right)\left(3a^2+1\right)\)
\(a^6-b^6=\left(a^3\right)^2-\left(b^3\right)^2=\left(a^3-b^3\right)\left(a^3+b^3\right)=\left(a-b\right)\left(a^2+ab+b^2\right).\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(a,\left(-64\right)+\left(x-3\right)^3\)
\(=\left(-4\right)^3+\left(x-3\right)^3\)
\(=\left(-4+x-3\right)\left[\left(-4\right)^2-\left(-4\right)\left(x-3\right)+\left(x-3\right)^2\right]\)
\(a,-64+\left(x-3\right)^3\)
\(=\left(-4\right)^3+\left(x-3\right)^3\)
\(=\left(-4+x-3\right)\left[\left(-4\right)^2-\left(-4\right)\left(x-3\right)+\left(x-3\right)^2\right]\)
\(=\left(x-7\right)\left(16+4x-12+x^2-6x+9\right)\)
\(=\left(x-7\right)\left(x^2-2x+13\right)\)