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CAPITULO VI

PRODUCTOS Y COCIENTES NOTABLES

Ejercicio 66

Desarrollar:

$\begin{matrix} {(a + 2)}^{3} & = {(a)}^{3} + 3 {(a)}^{2} (2) + 3 (a) {(2)}^{2} + {(2)}^{3} \\ = a^{3} + 6 a^{2} + 12 a + 8 \end{matrix}$
$\begin{matrix} {(x - 1)}^{3} & = {(x)}^{3} - 3 {(x)}^{2} (1) + 3 (x) {(1)}^{2} - {(1)}^{3} \\ = x^{3} - 3 x^{2} + 3 x - 1 \end{matrix}$
$\begin{matrix} {(m + 3)}^{3} & = {(m)}^{3} + 3 {(m)}^{2} (3) + 3 (m) {(3)}^{2} + {(3)}^{3} \\ = m^{3} + 9 m^{2} + 27 m + 27 \end{matrix}$
$\begin{matrix} {(n - 4)}^{3} & = {(n)}^{3} - 3 {(n)}^{2} (4) + 3 (n) {(4)}^{2} - {(4)}^{3} \\ = n^{3} - 12 n^{2} + 48 n - 64 \end{matrix}$
$\begin{matrix} {(2 x + 1)}^{3} & = {(2 x)}^{3} + 3 {(2 x)}^{2} (1) + 3 (2 x) {(1)}^{2} + {(1)}^{3} \\ = 8 x^{3} + 12 x^{2} + 6 x + 1 \end{matrix}$
$\begin{matrix} {(1 - 3 y)}^{3} & = {(1)}^{3} - 3 {(1)}^{2} (3 y) + 3 (1) {(3 y)}^{2} - {(3 y)}^{3} \\ = 1 - 9 y + 27 y^{2} - 27 y^{3} \end{matrix}$
$\begin{matrix} {(2 + y^{2})}^{3} & = {(2)}^{3} + 3 {(2)}^{2} (y^{2}) + 3 (2) {(y^{2})}^{2} + {(y^{2})}^{3} \\ = 8 + 12 y^{2} + 6 y^{4} + y^{6} \end{matrix}$
$\begin{matrix} {(1 - 2 n)}^{3} & = {(1)}^{3} - 3 {(1)}^{2} (2 n) + 3 (1) {(2 n)}^{2} - {(2 n)}^{3} \\ = 1 - 6 n + 12 n^{2} - 8 n^{3} \end{matrix}$
$\begin{matrix} {(4 n + 3)}^{3} & = {(4 n)}^{3} + 3 {(4 n)}^{2} (3) + 3 (4 n) {(3)}^{2} + {(3)}^{3} \\ = 64 n^{3} + 144 n^{2} + 108 n + 27 \end{matrix}$
$\begin{matrix} {(a^{2} - 2 b)}^{3} & = {(a^{2})}^{3} - 3 {(a^{2})}^{2} (2 b) + 3 (a^{2}) {(2 b)}^{2} - {(2 b)}^{3} \\ = a^{6} - 6 a^{4} b + 12 a^{2} b^{2} - 8 b^{3} \end{matrix}$
$\begin{matrix} {(2 x + 3 y)}^{3} & = {(2 x)}^{3} + 3 {(2 x)}^{2} (3 y) + 3 (2 x) {(3 y)}^{2} + {(3 y)}^{3} \\ = 8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3} \end{matrix}$
$\begin{matrix} {(1 - a^{2})}^{3} & = {(1)}^{3} - 3 {(1)}^{2} (a^{2}) + 3 (1) {(a^{2})}^{2} - {(a^{2})}^{3} \\ = 1 - 3 a^{2} + 3 a^{4} - a^{6} \end{matrix}$