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Deleted member 4993
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You read my mind .... you Yuri Geller you......No, that's not what he did because it doesn't work: (2x+ 2)+ (x+ 3)= (2x+x)+ (2+ 3)= 3x+ 5, not \(\displaystyle 2x^2+ 6X\)! If you meant (2x+ 2)(x+ 3), multiplying instead of adding? That's also wrong: \(\displaystyle (2x+ 2)(x+ 3)= 2x(x+ 3)+ 2(x+ 3)= 2x^2+ 6x+ 2x+ 6= 2x^2+ 8x+ 6\).
I can't speak for Subhotosh Khan's thought processes but I suspect he saw that there was an "x" both terms so he could factor out an "x". And he saw that both "2" and "6" are even numbers so he could factor out a "2". \(\displaystyle 2x^2+ 6x= x(2x+ 6)= 2x(x+ 3) \)