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Found: 3

Problem #PRU-115962

Problems Algebra Polynomials Algebraic identities for polynomials Factoring polynomials

12–14 2.0

Find $x^{3} + y^{3}$ if $x + y = 5$ and $x + y + x^{2} y + x y^{2} = 24$ .

Problem #PRU-116475

Problems Algebra Polynomials Algebraic identities for polynomials Factoring polynomials

12–14 2.0

Compute the following: $\frac{(2001 \times 2021 + 100) (1991 \times 2031 + 400)}{2011^{4}} .$

Problem #PRU-61001

Problems Algebra Polynomials Algebraic identities for polynomials Factoring polynomials

12–14 2.0

Prove the following formulae are true: $\begin{aligned} a^{n + 1} - b^{n + 1} & = (a - b) (a^{n} + a^{n - 1} b + \dots + b^{n}); \\ a^{2 n + 1} + b^{2 n + 1} & = (a + b) (a^{2 n} - a^{2 n - 1} b + a^{2 n - 2} b^{2} - \dots + b^{2 n}) . \end{aligned}$