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



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