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 corner:

Top right corner:

Bottom left corner:

Bottom right corner:

Add along the diagonal:

Combining our terms:

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.

Top left corner:

Top right corner:

Bottom left corner:

Bottom right corner:

Add along the pink diagonal:

Combining our terms:

Top left corner:

Top right corner:

Middle left:

Middle right:

Bottom left corner:

Bottom right corner:

Add along the first (pink) diagonal:

Add along the second (blue) diagonal:

Combining our terms:

Top left corner:

Top right corner:

Bottom left corner:

Bottom right corner:

Add along the (pink) diagonal:

Combining our terms, we get:

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.

To multiply two binomials, both terms in the first binomial need to be multiplied with both terms in the second binomial. A good way to make sure that all of the pairs are multiplied is to set up the box/grid:

In each empty box, multiply the intersecting terms:

Now, combine like terms. 3x and 8x are both terms with x, so we can add them to be 11x.

Final answer \[in descending order of powers of x:

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 .