The problem is to factor (x-1)(x+2)^2-(x-1)^2(X+2). I factored out (x-1)(x+2) creating (x-1)(x+2)[(x+2)-(X-1)]. Checking the answer guide, this is exactly what they did as well. However, they take a further step and end with 3(X-1)(X+2). I don't see how they reach this answer, and I'm beating my head against the wall trying to figure out how they got to this answer.
Looking at the expression I have after my initial factoring, if I multiply things out again I don't end up with three of the (X-1)(X+2) multiplied by each other, which seems to be what they are saying is the answer. I end up with (X-1)(x+2)(X+2)-(X-1)(X+2)(X-1), which I'm not really sure how to make sense of. The negative sign in the factored expression is particularly bothering me. I sort of see how the problem could work if there were a positive sign. (X-1)(X+2)(X+2)+(X-1)(X+2)(X-1) would leave me with three (x-1)(x-2)s. However, I don't have an expression with a positive sign, I have an expression with a negative sign after the initial factoring, and the answer key agrees with that step verbatim.
Any help figuring this out would be greatly appreciated! Thanks!
Looking at the expression I have after my initial factoring, if I multiply things out again I don't end up with three of the (X-1)(X+2) multiplied by each other, which seems to be what they are saying is the answer. I end up with (X-1)(x+2)(X+2)-(X-1)(X+2)(X-1), which I'm not really sure how to make sense of. The negative sign in the factored expression is particularly bothering me. I sort of see how the problem could work if there were a positive sign. (X-1)(X+2)(X+2)+(X-1)(X+2)(X-1) would leave me with three (x-1)(x-2)s. However, I don't have an expression with a positive sign, I have an expression with a negative sign after the initial factoring, and the answer key agrees with that step verbatim.
Any help figuring this out would be greatly appreciated! Thanks!
