Página — Matematica 8° Secundaria (pág. 145)

(2a^{2}+3b^{2})^{2}-4a^{2}b^{2}

\left(2a^{2}+3b^{2}+2a^{2}b^{2}\right)\left(2a^{2}+3b^{2}-2a^{2}b^{2}\right)

\left(2a^{2}+2a^{2}b^{2}+3b^{2}\right)\left(2a^{2}-2a^{2}b^{2}+3b^{2}\right)

Ejemplo 1

Desarrollo

Factorizamos

Sacamos la raiz de 4a^{2}b^{2} y la repartimos en cada uno de los términos sumándolo y restándolo pues se trata de una diferencia de cuadrados

Organizamos

\begin{aligned}\left(\overbrace{\begin{array}{c}{a^{4}-16a^{2}b^{2}+36b^{4}}\\ {\left|\begin{array}{c}{}\\ {}\\ {}\\ {}\\ \end{array}\right|}\\ {a^{2}}\\ {}\\ {}\\ \end{array}\right)}&{{}=a^{4}-16a^{2}b^{2}+36b^{4}+4a^{2}b^{2}-4a^{2}b^{2}}\\ {}&{{}=a^{4}-12a^{2}b^{2}+36b^{4}-4a^{2}b^{2}}\\ {}&{{}=(a^{4}-6b^{2})^{2}-4a^{2}b^{2}}\\ {}&{{}=(a^{2}-6b^{2}+2a b)(a^{2}-6b^{2}-2a b)}\\ {}&{{}}\\ {\quad\left.-2(a^{2})(6b^{2})\right.}\\ {}&{{}=(a^{2}-2a b-6b^{2})(a^{2}+2a b-6b^{2})}\\ {}&{{}=-12a^{2}b^{2}}\\ \end{aligned}

Ejemplo 2

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Matemáticas·Grado 8

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