\(x^3y^3+125=\left(xy+5\right)\left(x^2y^2-5xy+25\right)\)

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

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

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

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

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

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

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

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

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

Câu a : \(x^3y^3+225=\left(xy\right)^3+\left(\sqrt[3]{225}\right)^3=\left(xy+\sqrt[3]{225}\right)\left(x^2y^2-xy\sqrt[3]{225}+\left(\sqrt[3]{225}\right)^2\right)\)

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