How is 2(x-3)(x+2) + (x-3)^2 factored to (x-3)(2x+4+x-3)?

[fran1942]

Hello, I have this expression:
2(x-3)(x+2) + (x-3)^2

It is simplified to:

(x-3) (2x+4+x-3)


I understand how the (x-3) has been separated to start the simplification process, but I cannot grasp how the rest was done.
Can someone please tell me the rest was simplified ?

Thanks kindly for any help.

 

[cepheid]

Hello fran1942!

The first step is to factor out x-3 from both terms. In the left term, x-3 is multiplied by 2(x+2). In the right term, x-3 is multiplied by x-3. Therefore, if you factor out x-3, you are left with:

(x-3)[2(x+2) + x-3]

For the next step: in the first term in the square brackets, namely the 2(x+2) term, you can simply distribute the 2 amongst both of the terms that it is multiplied by: 2(x+2) = (2*x + 2*2) = 2x + 4. Therefore, you are left with:

(x-3)[2x+4 + x-3]