Ejercicio 62 – Solucionario Baldor

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CAPITULO VI

PRODUCTOS Y COCIENTES NOTABLES

Ejercicio 62

Escribir, por simple inspección, el resultado de:

$\begin{matrix} (m + 3)^{2} & = m^{2} + 2 (3) (m) + (3)^{2} \\ = m^{2} + 6 m + 9 \end{matrix}$
$\begin{matrix} (5 + x)^{2} & = (5)^{2} + 2 (5) (x) + (x)^{2} \\ = 25 + 10 x + x^{2} \end{matrix}$
$\begin{matrix} (6 a + b)^{2} & = (6 a)^{2} + 2 (6 a) (b) + (b)^{2} \\ = 36 a^{2} + 12 a b + b^{2} \end{matrix}$
$\begin{matrix} (9 + 4 m)^{2} & = (9)^{2} + 2 (9) (4 m) + (4 m)^{2} \\ = 81 + 72 m + 16 m^{2} \end{matrix}$
$\begin{matrix} (7 x + 11)^{2} & = (7 x)^{2} + 2 (7 x) (11) + (11)^{2} \\ = 49 x^{2} + 154 x + 121 \end{matrix}$
$\begin{matrix} (x + y)^{2} & = (x)^{2} + 2 (x) (y) + (y)^{2} \\ = x^{2} + 2 x y + y^{2} \end{matrix}$
$\begin{matrix} (1 + 3 x^{2})^{2} & = (1)^{2} + 2 (1) (3 x^{2}) + (b)^{2} \\ = 1 + 6 x^{2} + 9 x^{4} \end{matrix}$
$\begin{matrix} (2 x + 3 y)^{2} & = (2 x)^{2} + 2 (2 x) (3 y) + (3 y)^{2} \\ = 4 x^{2} + 12 x y + 9 y^{2} \end{matrix}$
$\begin{matrix} (a^{2} x + b y^{2})^{2} & = (a^{2} x)^{2} + 2 (a^{2} x) (b y^{2}) + (b y^{2})^{2} \\ = a^{4} x + 2 a^{2} b x y^{2} + b^{2} y^{4} \end{matrix}$
$\begin{matrix} (3 a^{3} + 8 b^{4})^{2} & = (3 a^{3})^{2} + 2 (3 a^{3}) (8 b^{4}) + (8 b^{4})^{2} \\ = 9 a^{6} + 48 a^{3} b^{4} + 64 b^{8} \end{matrix}$
$\begin{matrix} (4 m^{5} + 5 n^{6})^{2} & = (4 m^{5})^{2} + 2 (4 m^{5}) (5 n^{6}) + (5 n^{6})^{2} \\ = 16 m^{10} + 40 m^{5} n^{6} + 25 n^{12} \end{matrix}$
$\begin{matrix} (7 a^{2} b^{3} + 5 x^{4})^{2} & = (7 a^{2} b^{3})^{2} + 2 (7 a^{2} b^{3}) (5 x^{4}) + (5 x^{4})^{2} \\ = 49 a^{4} b^{6} + 70 a^{2} b^{3} x^{4} + 25 x^{8} \end{matrix}$
$\begin{matrix} (4 a b^{2} + 5 x y^{3})^{2} & = (4 a b^{2})^{2} + 2 (4 a b^{2}) (5 x y^{3}) + (5 x y^{3})^{2} \\ = 16 a^{2} b^{4} + 40 a b^{2} x y^{3} + 25 x^{2} y^{6} \end{matrix}$
$\begin{matrix} (8 x^{2} y + 9 m^{3})^{2} & = (8 x^{2} y)^{2} + 2 (8 x^{2} y) (9 m^{3}) + (9 m^{3})^{2} \\ = 64 x^{4} y^{2} + 144 m^{3} x^{2} y + 81 m^{6} \end{matrix}$
$\begin{matrix} (x^{10} + 10 y^{12})^{2} & = (x^{10})^{2} + 2 (x^{10}) (10 y^{12}) + (x^{10})^{2} \\ = x^{20} + 20 x^{10} y^{12} + 100 y^{24} \end{matrix}$
$\begin{matrix} (a^{m} + a^{n})^{2} & = (a^{m})^{2} + 2 (a^{m}) (a^{n}) + (a^{n})^{2} \\ = a^{2 m} + 2 a^{m + n} + a^{2 n} \end{matrix}$
$\begin{matrix} (a^{x} + b^{x + 1})^{2} & = (a^{x})^{2} + 2 (a^{x}) (b^{x + 1}) + (b^{x + 1})^{2} \\ = a^{2 x} + 2 a^{x} b^{x + 1} + b^{2 x + 2} \end{matrix}$
$\begin{matrix} (x^{a + 1} + y^{x - 2})^{2} & = (x^{a + 1})^{2} + 2 (x^{a + 1}) (y^{x - 2}) + (y^{x - 2})^{2} \\ = x^{2 a + 2} + 2 x^{a + 1} y^{x - 2} + y^{2 x - 4} \end{matrix}$