Let's look at the grid for  first.

Now let's look at the grid for .

Top left corner:

  or 

Both grids give us .

Top right corner:

 or 

Bottom left corner:

 or 

Bottom right corner:

 or 

Both grids give us  here.

Add along the (pink) diagonals in each grid:

 or 

Both grids give us .

Combining our terms in either grid, we get:

So the answers are exactly the same!

Top left corner:

Top right corner:

Bottom left corner:

Bottom right corner:

Add along the (pink) diagonal:

Combining our terms, we get:

Top left corner:

Top right corner:

Bottom left corner:

Bottom right corner:

Add along the (pink) diagonal:

Combining our terms, we get:

Top left: 

Top middle: 

Top right: 

Bottom left: 

Bottom middle: 

Bottom right: 

Add along the first (pink) diagonal: 

Add along the second (blue) diagonal: 

Combining our terms, we get .

Top left: 

Top right: 

Middle left: 

Middle right: 

Bottom left: 

Bottom right: 

Add along the first (pink) diagonal: 

Add along the second (blue) diagonal: 

Combining our terms, we get .

Top left: 

Top middle: 

Top right: 

Middle left: 

Center block: 

Middle right: 

Bottom left: 

Bottom middle: 

Bottom right: 

Add along the first (pink) diagonal: 

Add along the second (blue) diagonal: 

Add along the third (orange) diagonal: 

Combining our terms, we get  or

.

Top left: 

Top middle: 

Top right: 

Middle left: 

Center block: 

Middle right: 

Bottom left: 

Bottom middle: 

Bottom right: 

Add along the first (pink) diagonal: 

Add along the second (blue) diagonal: 

Add along the third (orange) diagonal: 

Combining our terms, we get .

This question is merely asking us to complete the grid form of FOIL and find the final result. 

In order to complete the four squares, we merely multiply the term above the box in the topmost row by the term in the leftmost column. 

For example, in order to solve for the top left box:

multiplying 

Moving on to the bottom left box, using the same principle, we would get 

multiplying 

The same principles can be applied with the two right boxes. Multiplying the terms will yield a filled in grid that looks like this:

The next step involves us to use the information from the four boxes and collect like terms to get our final answer:

To solve using the grid method, we use the given problem

and create a grid using each term.

Now, we fill in the boxes by multiplying the terms in each row and column.

Now, we write each of the multiplied terms out,

We combine like terms.

Therefore, by using the grid method, we get the solution

Using the grid method is an alternate way of doing FOIL. This utilizes the "tic tac toe" grid. Upon creating the grid, we need to write in the binomials we were given to multiply. Such is done like so:

 and  have been written in on the leftmost column and topmost row as separated terms. In order to carry out FOIL, we must now fill in the four remaining boxes. In order to do so, each box will be solved by mutlipyling the term above it in the topmost row by the term next to it in the leftmost column. For example, the top left box will be filled in by multiplying .

Using the same principle, the left bottom box will be completed by multiplying , like so:

The remaining boxes in the rightmost column may be solved using the same principle that was used to solve for the middle column. The filled out grid will look like this:

The problem is nearly done. All that is left for us to do is to write this as a mathematical expression and collect like terms. Completing this step will yield us our final answer. 

Note that this last step only requires the values from the four boxes we solved for.