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which of the following expressions is equal is equivalent to 7 K 7 K minus minus the product of K plus 1 and 2 k plus 2 all right so this is going to be 7 K minus 7 K minus the product of k plus 1 & 2 k plus 2 and so let's see though to kind of expand it all out we will want to multiply these two expressions so let's do that first so it's going to be this is going to be 7 K minus minus and then let's just multiply this out you're gonna have K times 2 K which is 2 K squared K times 2 which is going to be plus 2 K then 1 times 2 K which is going to give us another 2 K and then 1 times 2 which is going to give us plus 2 so and we want to be careful we want to put a parenthesis out front cuz it's gonna be we're gonna subtract all of this stuff right over here so this is going to be the same thing as 7 K minus 7 K minus and then in parenthesis we have 2 K squared we can add 2 k plus 2 K to get 4 K plus 4 k plus 2 and now we can one way to think about it is we can distribute this negative sign or you could even view this as minus 1 times all of this and so this is going to be the same thing as 7 K minus 2 K squared so minus 2 K squared 2 K squared minus 4 K minus 4 K and then minus 2 minus 2 and let's see so if we if we write the highest degree term first if we write this term they're just in a different color if we were to write this term first you get negative 2k squared that's our highest degree term and actually immediately when you look at the choices only one of these start with negative 2k squared has negative 2 is the coefficient on the K squared term so we already know that that one's going to be the choice but let's just confirm it so it's negative 2k squared and then we could add we could add 7k and negative 4k those who are going to add 7 minus 4 so I'm think it's going to be 3 of that so gonna be plus 3k which is what we see right over there and then finally you have this minus 2 minus 2 which is exactly what we see in this first choice up here