C. Multiplying Binomials

It is possible to use grid multiplication to multiply binomials.

Investigation

1. The following shows grid multiplication using algebra tiles.
   
   
   
   

2. 
   

1. State the two binomial expressions that are being multiplied.
   
   

2. There are four simpler products shown in the diagram. One of these is . State the other three.
   
   

3. What is the final product of this multiplication?
   
   

3. 
   

   1. Use algebra tiles and grid multiplication to determine the product of .
      
      

   2. Substitute 5 for x in , and evaluate.
      
      

   3. Substitute 5 for x in the expression you determined in a., and evaluate.
      
      

   4. Compare the values from b. and c.
      
      

4. Using patterns observed in this investigation and the one before it, explain how you could multiply without using algebra tiles.