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Problems Algebra Algebraic equations and systems of equations Binomial theorem Higher order equations. Palindromic polynomial equations Equations of higher order (other)

12–14 2.0

Prove the validity of the following formula of Newton’s binom $(x + y)^{n} = (\binom{n}{0}) x^{n} + (\binom{n}{1}) x^{n - 1} y + \dots + (\binom{n}{n}) y^{n} .$

Problem #PRU-60389

Problems Algebra Algebraic equations and systems of equations Binomial theorem

14–16 3.0

How many rational terms are contained in the expansion of

a) $(\sqrt{2} + \sqrt[4]{3})^{100}$ ;

b) $(\sqrt{2} + \sqrt[3]{3})^{300}$ ?