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

\(\left(a-1\right)^3-\left(a+1\right)^3=a^3-3a^2+3a-1-a^3-3a^2-3a-1=-6a^2-2=-2\left(3a^2+1\right)\)

\(a,\left(4-xy\right)^3\)

\(=4^3-3.4^2xy+3.4.x^2y^2-x^3y^3\)

\(=64-48xy+12x^2y^2-x^3y^3\)

\(b,\left(0,1+xy\right)^3\)

\(=\left(0,1\right)^3+3.\left(0,1\right)^2xy+3.0,1.\left(xy\right)^2+x^3y^3\)

\(=0,001+0,03xy+0,3x^2y^2+x^3y^3\)

\(\left(a-1\right)^3-\left(a+1\right)^3\)

\(=\left[\left(a-1\right)-\left(a+1\right)\right]\left[\left(a-1\right)^2+\left(a-1\right)\left(a+1\right)+\left(a+1\right)^2\right]\)

\(=\left(-2\right)\left(a^2-2a+1+a^2-1+a^2+2a+1\right)\)

\(=\left(-2\right)\left(3a^2+1\right)\)

\(a^6-b^6=\left(a^3\right)^2-\left(b^3\right)^2=\left(a^3-b^3\right)\left(a^3+b^3\right)=\left(a-b\right)\left(a^2+ab+b^2\right).\left(a+b\right)\left(a^2-ab+b^2\right)\)

\(a,\left(-64\right)+\left(x-3\right)^3\)

\(=\left(-4\right)^3+\left(x-3\right)^3\)

\(=\left(-4+x-3\right)\left[\left(-4\right)^2-\left(-4\right)\left(x-3\right)+\left(x-3\right)^2\right]\)

\(a,-64+\left(x-3\right)^3\)

\(=\left(-4\right)^3+\left(x-3\right)^3\)

\(=\left(-4+x-3\right)\left[\left(-4\right)^2-\left(-4\right)\left(x-3\right)+\left(x-3\right)^2\right]\)

\(=\left(x-7\right)\left(16+4x-12+x^2-6x+9\right)\)

\(=\left(x-7\right)\left(x^2-2x+13\right)\)