Expanding Brackets - Quadratic Factors

by Fawn
(United States)

Question

Expand (y+1)(y-3).

Answer

Before we expand (y+1)(y-3), let's take a look at the basic ideas behind removing brackets for p(y-3). We should know that:

p(y-3)
    = yp -3p

After knowing the above, let's see how this can be used to
expand (y+1)(y-3). Now, notice that if we let p = (y+1), we have:

p(y-3)
            = (y+1)(y-3)

Therefore:

Since,    p(y-3) = yp -3p
       Hence,   (y+1)(y-3) = y(y+1) -3(y+1) 

 From here, we can continue to simplify:

   (y+1)(y-3) = y(y+1) -3(y+1)
               = y² + y -3y -3
                = y² -2y -3       

We can no longer able to simplify further, therefore:

   (y+1)(y-3)
   = y² -2y -3