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CAPITULO VI

PRODUCTOS Y COCIENTES NOTABLES

Ejercicio 67

Escribir, por simple inspección, el resultado de:

$\begin{matrix} (a + 1) (a + 2) & = {(a)}^{2} + (1 + 2) (a) + (1 \times 2) \\ = a^{2} + 3 a + 2 \end{matrix}$
$\begin{matrix} (x + 2) (x + 4) & = {(x)}^{2} + (2 + 4) (x) + (2 \times 4) \\ = x^{2} + 6 x + 8 \end{matrix}$
$\begin{matrix} (x + 5) (x - 2) & = {(x)}^{2} + (5 - 2) (x) + [5 (- 2)] \\ = x^{2} + 3 x - 10 \end{matrix}$
$\begin{matrix} (m - 6) (m - 5) & = {(m)}^{2} + (- 6 - 5) (m) + [(- 6) (- 5)] \\ = m^{2} - 11 m + 30 \end{matrix}$
$\begin{matrix} (x + 7) (x - 3) & = {(x)}^{2} + (7 - 3) (x) + [7 (- 3)] \\ = x^{2} + 4 x - 21 \end{matrix}$
$\begin{matrix} (x + 2) (x - 1) & = {(x)}^{2} + (2 - 1) (x) + [2 (- 1)] \\ = x^{2} + x - 2 \end{matrix}$
$\begin{matrix} (x - 3) (x - 1) & = {(x)}^{2} + (- 3 - 1) (x) + [(- 3) (- 1)] \\ = x^{2} - 4 x + 3 \end{matrix}$
$\begin{matrix} (x - 5) (x + 4) & = {(x)}^{2} + (- 5 + 4) (x) + [(- 5) \times 4] \\ = x^{2} - x - 20 \end{matrix}$
$\begin{matrix} (a - 11) (a + 10) & = {(a)}^{2} + (- 11 + 10) (a) + [(- 11) \times 10] \\ = a^{2} - a - 110 \end{matrix}$
$\begin{matrix} (n - 19) (n + 10) & = {(n)}^{2} + (- 19 + 10) (n) + [(- 19) \times 10] \\ = n^{2} - 9 n - 190 \end{matrix}$
$\begin{matrix} (a^{2} + 5) (a^{2} - 9) & = {(a^{2})}^{2} + (5 - 9) (a^{2}) + [5 (- 9)] \\ = a^{4} - 4 a^{2} - 45 \end{matrix}$
$\begin{matrix} (x^{2} - 1) (x^{2} - 7) & = {(x^{2})}^{2} + (- 1 - 7) (x^{2}) + [(- 1) (- 7)] \\ = x^{4} - 8 x^{2} + 7 \end{matrix}$
$\begin{matrix} (n^{2} - 1) (n^{2} + 20) & = {(n^{2})}^{2} + (- 1 + 20) (n^{2}) + [(- 1) \times 20] \\ = n^{4} + 19 n^{2} - 20 \end{matrix}$
$\begin{matrix} (n^{3} + 3) (n^{3} - 6) & = {(n^{3})}^{2} + (+ 3 - 6) (n^{3}) + [3 (- 6)] \\ = n^{6} - 3 n^{3} - 18 \end{matrix}$
$\begin{matrix} (x^{3} + 7) (x^{3} - 6) & = {(x^{3})}^{2} + (7 - 6) (x^{3}) + [7 (- 6)] \\ = x^{6} + x^{3} - 42 \end{matrix}$
$\begin{matrix} (a^{4} + 8) (a^{4} - 1) & = {(a^{4})}^{2} + (8 - 1) (a^{4}) + [8 (- 1)] \\ = a^{8} + 7 a^{4} - 8 \end{matrix}$
$\begin{matrix} (a^{5} - 2) (a^{5} + 7) & = {(a^{5})}^{2} + (- 2 + 7) (a^{5}) + [(- 2) \times 7] \\ = a^{10} + 5 a^{5} - 14 \end{matrix}$
$\begin{matrix} (a^{6} + 7) (a^{6} - 9) & = {(a^{6})}^{2} + (7 - 9) (a^{6}) + [7 (- 9)] \\ = a^{12} - 2 a^{6} - 63 \end{matrix}$
$\begin{matrix} (a b + 5) (a b - 6) & = {(a b)}^{2} + (5 - 6) (a b) + [5 (- 6)] \\ = a^{2} b^{2} - a b - 30 \end{matrix}$
$\begin{matrix} (x y^{2} - 9) (x y^{2} + 12) & = {(x y^{2})}^{2} + (- 9 + 12) (x y^{2}) + [(- 9) \times 12] \\ = x^{2} y^{4} + 3 x y^{2} - 108 \end{matrix}$
$\begin{matrix} (a^{2} b^{2} - 1) (a^{2} b^{2} + 7) & = {(a^{2} b^{2})}^{2} + (- 1 + 7) (a^{2} b^{2}) + [(- 1) \times 7] \\ = a^{4} b^{4} + 6 a^{2} b^{2} - 7 \end{matrix}$
$\begin{matrix} (x^{3} y^{3} - 6) (x^{3} y^{3} + 8) & = {(x^{3} y^{3})}^{2} + (- 6 + 8) (x^{3} y^{3}) + [(- 6) \times 8] \\ = x^{6} y^{6} + 2 x^{3} y^{3} - 48 \end{matrix}$
$\begin{matrix} (a^{x} - 3) (a^{x} + 8) & = {(a^{x})}^{2} + (- 3 + 8) (a^{x}) + [(- 3) \times 8] \\ = a^{2 x} + 5 a^{x} - 24 \end{matrix}$
$\begin{matrix} (a^{x + 1} - 6) (a^{x + 1} - 5) & = {(a^{x + 1})}^{2} + (- 6 - 5) (a^{x + 1}) + [(- 6) (- 5)] \\ = a^{2 x + 2} - 11 a^{x + 1} + 30 \end{matrix}$