What's the solution to (x-2)(x-7)+(x-2)(x-7)?

Question

I'm having trouble trying to solve this problem. I know about special products but I don't know how to solve this. Please, help.

Answer 1

If you were asked to solve 3 + 3, you would answer 6. Similarly, 4 + 4 = 8, 5 + 5 = 10, etc. Each time, you're adding something to itself and you wind up with two times the original thing:

 

3 + 3 = 3×2 = 6

4 + 4 = 4×2 = 8

5 + 5 = 5×2 = 10

 

In the same way, you could say that x + x = 2x. Something plus itself is two times that thing.

 

Here, you're actually doing the same thing. (x-2)(x-7) plus itself.

 

So, your expression is also equal to:

 

2(x-2)(x-7)

 

You can solve that by foiling first, then distributing the 2:

 

2(x² - 7x - 2x + 14)

2(x² - 9x + 14)

2x² - 18x + 28