Factorizar por factor comun?

Bueno vamos a usar éstos casos de factoreo, , ,

<img src="https://tex.z-dn.net/?f=ad%2Bcd%2B%28a%2Bc%29%20%5C%5C%20d%28a%2Bc%29%2B%28a%2Bc%29%20%5C%5C%20%28a%2Bc%29%28d%2B1%29" />

Ahora empecemos :

<img src="https://tex.z-dn.net/?f=i%29%20%5C%5C%202a%5E%7B2%7D%20-4ab-5a%2B10b%20%5C%5C%20%282%20a%5E%7B2%7D-4ab%20%29%2B%28-5a%2B10b%29%20%5C%5C%202a%28a-2b%29-5%28a-2b%29%20%5C%5C%20%28a-2b%29%282a-5%29%20%5C%5C%20%20%5C%5C%20ii%29%20%5C%5C%207a%20b%5E%7B2%7D%20%2Bac-14b%5E%7B2%7D%20xy-2cxy%20%5C%5C%20%287a%20b%5E%7B2%7D%20-14b%5E%7B2%7D%20xy%29%2B%28ac-2cxy%29%20%5C%5C%207%20b%5E%7B2%7D%20%28a-2xy%29%2Bc%28a-2xy%29%20%5C%5C%20%28a-2xy%29%287%20b%5E%7B2%7D%2Bc%20%29%20%5C%5C%20%20%5C%5C%20iii%29%20%20%5C%5C%20x%5E%7B2%7D%20%20y%5E%7B3%7D%20%2B5y%5E%7B3%7D-3%20x%5E%7B2%7D%20-15%20%5C%5C%20%28x%5E%7B2%7D%20%20y%5E%7B3%7D-3%20x%5E%7B2%7D%20%29%2B%285y%5E%7B3%7D-15%29%20%5C%5C%20%20x%5E%7B2%7D%20%28%20y%5E%7B3%7D%20-3%29%2B5%28y%5E%7B3%7D%20-3%29%20%5C%5C%20%28%20y%5E%7B3%7D-3%20%29%28x%5E%7B2%7D%20%2B5%29%20%5C%5C%20%20%5C%5C%20iv%29%20%5C%5C%205ab-10-5x-abc%5E%7B2%7D%20%2B2%20c%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20x%20%5C%5C%20%285ab-10-5x%29%2B%28-abc%5E%7B2%7D%2B2%20c%5E%7B2%7D%2B%20c%5E%7B2%7Dx%20%20%29%20%5C%5C%205%28ab-2-x%29-%20c%5E%7B2%7D%20%28ab-2-x%29%20%5C%5C%20%28ab-2-x%29%285-c%5E%7B2%7D%20%29" />

<img src="https://tex.z-dn.net/?f=v%29%20%5C%5C%20%20a%5E%7B2%7D%20%20x%5E%7B2%7D%20-%20b%5E%7B3%7D%20%20x%5E%7B2%7D%20%2B%20x%5E%7B2%7D%20-%20a%5E%7B2%7D%20bc%2B%20b%5E%7B4%7D%20c-bc%20%5C%5C%20%28a%5E%7B2%7D%20%20x%5E%7B2%7D%20-%20b%5E%7B3%7D%20%20x%5E%7B2%7D%20%2B%20x%5E%7B2%7D%29%2B%28-%20a%5E%7B2%7D%20bc%2B%20b%5E%7B4%7D%20c-bc%20%29%20%5C%5C%20%20x%5E%7B2%7D%20%28%20a%5E%7B2%7D-%20b%5E%7B3%7D%2B1%20%20%29-bc%28%20a%5E%7B2%7D-b%20%5E%7B3%7D%20%2B1%20%29%20%5C%5C%20%28%20a%5E%7B2%7D-%20b%5E%7B3%7D%2B1%20%20%29%28%20x%5E%7B2%7D%20-bc%29%20%5C%5C%20%20%5C%5C%20vi%29%20%5C%5C%203%20a%5E%7B2%7D%20x-3%20b%5E%7B2%7D%20x-3x-%20a%5E%7B2%7D%2B%20b%5E%7B2%7D%20%20%2B1%20%5C%5C%20%283%20a%5E%7B2%7D%20x-3%20b%5E%7B2%7D%20x-3x%29%2B%28-%20a%5E%7B2%7D%2B%20b%5E%7B2%7D%20%20%2B1%29%20%5C%5C%203x%28%20a%5E%7B2%7D-%20b%5E%7B2%7D%20-1%20%29-%28%20a%5E%7B2%7D-%20b%5E%7B2%7D-1%20%20%29%20%5C%5C%20%28%20a%5E%7B2%7D-%20b%5E%7B2%7D-1%20%20%29%283x-1%29%20%5C%5C%20%20%5C%5C%20vii%29%20%5C%5C%2010a-15b-20%2B6ax-9bx-12x%20%5C%5C%20%2810a-15b-20%29%2B%286ax-9bx-12x%29%20%5C%5C%205%282a-3b-4%29%2B3x%282a-3b-4%29%20%5C%5C%20%282a-3b-4%29%285%2B3x%29" />

Y eso sería todo.

Espero te sirva y si tienes alguna duda me avisas

Nota : primero agrupamos los términos a nuestra conveniencia.

Y sacamos factor común.