Matemática: Identidades algebraicas y factorización (cúbicos y cuadrados)

Anotacoes

N 12 1 2 3 4 BUREAU 22. $\frac{1^{\text{op}} + 2^{\text{op}} + 3^{\text{op}} + 4^{\text{op}} + 5^{\text{op}}}{\text{ DIVISION}}$ PAR 5. $$ \begin{array}{l} 1^{\text{op}} + 4^{\text{op}} = (1 + 4) \left( \underline{1 - 4 + 4^{\text{op}} - \cdots - 4^{\text{op}}} \right) = M(5) \\ 2^{\text{op}} + 3^{\text{op}} = (2 + 3) \left( 2^{\text{op}} - \cdots - 3^{\text{op}} \right) = M(5) \end{array} \quad \left\{ \begin{array}{l} M^{(1)}(5) \\ \end{array} \right. $$ $$ \begin{array}{l} a^3 + b^3 = (a + b)(a^2 - ab + b^2) \\ a^2 + b^2 = (a + b)(a^4 - a^2b + a^2b^2 - ab^2) \\ a^2 + b^2 = (a + b)(a^6 - a^2b + a^4b^2 - a^2b^2) \\ \end{array} $$   $$ \begin{array}{l} a^{3} + b^{3} = (a + b)(a^{2} - ab + b^{2}) \\ a^{2} + b^{2} = (a + b)(a^{4} - a^{2}b + a^{2}b^{2} - ab^{3} + b^{4}) \\ a^{2} + b^{2} = (a + b)(a^{6} - a^{2}b + a^{4}b^{2} - a^{3}b^{3} + a^{2 + b} - ab^{2} + b^{6}) \\ \end{array} \quad \left\{ \begin{array}{l} \text{n. 1.} \end{array} \right. $$   a) $a + b + c = 0 \Rightarrow a^2 + b^2 + c^2 = 3abc$ $$ \begin{array}{l} x = a - b \\ y = b - c \\ z = c - a \\ \end{array} $$ $$ \begin{ar...