Starting with the very first question
[tex] \sf \: ax + bx - ay - by \\ \sf \: ax - ay + bx - by \\ \sf \: a(x - y) + b(x - y) \\ \bf \mapsto\: (a + b)(x - y)[/tex]
Second one
[tex] \sf \: 15pq + 25p + 9q + 15 \\ \sf \: 5p(3q + 5) + 3(3q + 5) \\ \bf \mapsto \: (5p + 3)(3q +5 )[/tex]
Third one
[tex] \sf \: z - 7 - xyz + 7xy \\ \sf \: (z - 7) - xy(z - 7) \\ \bf \mapsto(z - 7)(1 - xy)[/tex]
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Verified answer
Starting with the very first question
[tex] \sf \: ax + bx - ay - by \\ \sf \: ax - ay + bx - by \\ \sf \: a(x - y) + b(x - y) \\ \bf \mapsto\: (a + b)(x - y)[/tex]
Second one
[tex] \sf \: 15pq + 25p + 9q + 15 \\ \sf \: 5p(3q + 5) + 3(3q + 5) \\ \bf \mapsto \: (5p + 3)(3q +5 )[/tex]
Third one
[tex] \sf \: z - 7 - xyz + 7xy \\ \sf \: (z - 7) - xy(z - 7) \\ \bf \mapsto(z - 7)(1 - xy)[/tex]