# Algebra 1 : How to use the grid method for FOIL

## Example Questions

Explanation:

### Example Question #1 : How To Use The Grid Method For Foil

Multiply:

Explanation:

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:

### Example Question #2 : How To Use The Grid Method For Foil

Multiply:

Explanation:

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. -6x and 4x are both terms with x, so we can add them to be -2x.

### Example Question #1 : How To Use The Grid Method For Foil

Use the grid method to distribute and simply .

Explanation:

Top left corner:

Top right corner:

Bottom left corner:

Bottom right corner:

Add along the diagonal:

Combining our terms:

### Example Question #1 : How To Use The Grid Method For Foil

Expand  using the grid method.

Explanation:

Top left corner:

Top right corner:

Bottom left corner:

Bottom right corner:

Add along the pink diagonal:

Combining our terms:

### Example Question #3 : How To Use The Grid Method For Foil

Expand  using the grid method.

Explanation:

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:

### Example Question #4 : How To Use The Grid Method For Foil

Expand  using the grid method.

Explanation:

Top left corner:

Top right corner:

Bottom left corner:

Bottom right corner:

Add along the (pink) diagonal:

Combining our terms:

### Example Question #8 : How To Use The Grid Method For Foil

Expand  using the grid method.

Explanation:

Top left corner:

Top right corner:

Bottom left corner:

Bottom right corner:

Add along the (pink) diagonal:

Combining our terms:

### Example Question #9 : How To Use The Grid Method For Foil

Expand  and  using the grid method. Compare your answers.

The answers are the same.

The answers are completely different.

The answers are the same except that the middle terms are different.

The answers have opposite signs.

The answers are the same.

Explanation:

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!

### Example Question #5 : How To Use The Grid Method For Foil

Expand  using the grid method.

Explanation:

Top left corner:

Top right corner:

Bottom left corner:

Bottom right corner:

Add along the (pink) diagonal:

Combining our terms, we get: