Simplificar al maximo ejercicio de productos notables(4yw - 12xp + 8yp - 6xw)(4y2 - 16x2) / ( - 12x2 + 14xy - 4y2)?

Al simplificar al máximo la expresión nos queda : <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%284yw-12xp%2B8yp-6xw%5Cright%29%5Cleft%284y%5E2-16x%5E2%5Cright%29%7D%7B-12x%5E2%2B14xy-4y%5E2%7D%3D-4%5Cleft%28w%2B2p%5Cright%29%5Cleft%28y%2B2x%5Cright%29" />Expliación : Primero nos enfocamos en el numerador : <img src="https://tex.z-dn.net/?f=4yw-12xp%2B8yp-6xw%3D2%5Cleft%28w%2B2p%5Cright%29%5Cleft%282y-3x%5Cright%29" /> (Sacamos factor común 2)<img src="https://tex.z-dn.net/?f=4y%5E2-16x%5E2%3D4%5Cleft%28y%5E2-4x%5E2%5Cright%29" /> (Sacamos factor común 4)Nos queda entonces en el numerador : <img src="https://tex.z-dn.net/?f=%5Cleft%284yw-12xp%2B8yp-6xw%5Cright%29%5Cleft%284y%5E2-16x%5E2%5Cright%29%3D%208%5Cleft%28w%2B2p%5Cright%29%5Cleft%282y-3x%5Cright%29%5Cleft%28y%5E2-4x%5E2%5Cright%29" />Ahora vemos el denominador : <img src="https://tex.z-dn.net/?f=-12x%5E2%2B14xy-4y%5E2%20%3D%20-2%5Cleft%282y-3x%5Cright%29%5Cleft%28y-2x%5Cright%29" />La expresión completa nos queda : <img src="https://tex.z-dn.net/?f=%3D-%5Cfrac%7B4%5Cleft%28w%2B2p%5Cright%29%5Cleft%282y-3x%5Cright%29%5Cleft%28y%5E2-4x%5E2%5Cright%29%7D%7B%5Cleft%28y-2x%5Cright%29%5Cleft%282y-3x%5Cright%29%7D" />Podemos simplificar términos comunes del numerador y denominador : <img src="https://tex.z-dn.net/?f=%3D-%5Cfrac%7B4%5Cleft%28w%2B2p%5Cright%29%5Cleft%28y%5E2-4x%5E2%5Cright%29%7D%7By-2x%7D" />Factorizamos nuevamente en el numerador : <img src="https://tex.z-dn.net/?f=y%5E2-4x%5E2%3D%20%5Cleft%28y%2B2x%5Cright%29%5Cleft%28y-2x%5Cright%29" />Nos queda : <img src="https://tex.z-dn.net/?f=%3D-%5Cfrac%7B4%5Cleft%28w%2B2p%5Cright%29%5Cleft%28y%2B2x%5Cright%29%5Cleft%28y-2x%5Cright%29%7D%7By-2x%7D" /><img src="https://tex.z-dn.net/?f=%3D-4%5Cleft%28w%2B2p%5Cright%29%5Cleft%28y%2B2x%5Cright%29" />Puedes ver otro ejercicio de factorización aquí : brainly.

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