1.3-bo'lim : Radikallar
15. Quyidagi ifodani ko‘paytiring. \(x\) ijobiy deb faraz qiling.
\[\left( {\sqrt[3]{x} + 2\,\,\sqrt[3]{{{x^2}}}} \right)\left( {4 - \sqrt[3]{{{x^2}}}} \right)\]Yechim
Bu erda qilishimiz kerak bo'lgan yagona narsa ko'paytirishni bajarishdir, shuning uchun bu erda.
\[\begin{align*}\left( {\sqrt[3]{x} + 2\,\,\sqrt[3]{{{x^2}}}} \right)\left( {4 - \sqrt[3]{{{x^2}}}} \right) & = 4\sqrt[3]{x} - \sqrt[3]{x}\,\,\sqrt[3]{{{x^2}}} + 8\,\,\sqrt[3]{{{x^2}}} - 2\,\,\sqrt[3]{{{x^2}}}\,\,\sqrt[3]{{{x^2}}}\\ & = 4\sqrt[3]{x} - \sqrt[3]{{{x^3}}} + 8\,\,\sqrt[3]{{{x^2}}} - 2\,\,\sqrt[3]{{{x^4}}}\\ & = 4\sqrt[3]{x} - \sqrt[3]{{{x^3}}} + 8\,\,\sqrt[3]{{{x^2}}} - 2\,\,\sqrt[3]{{{x^3}}}\,\,\sqrt[3]{x}\\ & = \require{bbox} \bbox[2pt,border:1px solid black]{{4\sqrt[3]{x} - x + 8\,\,\sqrt[3]{{{x^2}}} - 2x\,\,\sqrt[3]{x}}}\end{align*}\]Bo'lishi mumkin bo'lgan har qanday natijada ildizlarni soddalashtirishni unutmang. Bu ko'pincha ushbu muammolarning o'tkazib yuborilgan qismidir va kvadrat ildizlardan tashqari ildizlar bilan ishlashda, biz ushbu muammo bilan ko'rganimizdek, soddalashtirish jarayonida biroz ish bo'lishi mumkin.