Question

Ayudenme por favor Desarrollo de  Binomio de newton
$( x^{7} - \sqrt[3]{x} ) ^{4}$

Answer 1

Utiliza la formula del binomio a la cuarta.

$(a-b)^4=a^4-4a^3b^+6a^2b^2-4ab^3+b^4\\ \\a=x^7\\b= \sqrt[3]{x}\\ \\(x^7-\sqrt[3]{x})^4=(x^7)^4-4(x^7)^3(\sqrt[3]{x})+6(x^7)^2(\sqrt[3]{x})^2-4(x^7)(\sqrt[3]{x})^3+(\sqrt[3]{x})^4\\ \\ (x^7-\sqrt[3]{x})^4=x^{28}-4x^{21}x^{\frac{1}{3}}+6x^{14}x^{\frac{2}{3}}-4x^7x^{\frac{3}{3}}+x^{\frac{4}{3}}\\ \\(x^7-\sqrt[3]{x})^4=x^{28}-4x^{\frac{64}{3}}+6x^{\frac{44}{3}}-4x^8+x^{\frac{4}{3}}\\ \\(x^7-\sqrt[3]{x})^4=x^{28}-4x^8-4x^{\frac{64}{3}}+6x^{\frac{44}{3}}+x^{\frac{4}{3}}$