How to FOIL

FOILing is a simple trick used to multiply two polynomials together. FOIL stands for the order in which the terms of the polynomials are multiplied. F is for First, O is for Outside, I is for Inside and L is for Last.

(3x + 4) * (2x - 8)

Multiply the first terms- This would be 6x2.

Multiply the outside terms- This would be -24x.

Multiply the inside terms- This would be 8x.

Multiply the last terms- This would be -32.

Then combine like terms. The final result is 6x2 -16x - 32.

This same principle can be applied to polynomials that have more than 2 terms. Just be sure to multiply the first term in the first polynomial by all of the terms in the second polynomial. Then multiply the second term of the first polynomial by all of the terms in the second polynomial and so on.

(2x2 + 6x - 4) * (5x + 1)

Multiple 2x2 by all of the terms in the second polynomial. This is 10x3 + 2x2.

Next multiply 6x by all of the terms in the second polynomial. This is 30x2 + 6x.

Finally, multiply -4 by all of the terms in the second polynomial. This is -20x -4.

The total product is now 10x3 + 2x2 + 30x2 + 6x -20x -4.

Combine like terms and the final answer becomes 10x3 + 32x2 -14x -4.

Try this one on your own.

(4x2 + 5x + 2) * (x2 + 8)

Did you get 4x4 + 5x3 + 34x2 + 40x + 16? If so, you are correct!

FOIL Method for Multiplying Binomials

Box Method

The box method is a visual that enables you to see that you did all the necessary multiplication. If you are multiplying two binomials together, a four square appearing box is made. Then one binomial is placed across the top and the other goes on the left side. The box method works for multiplying any expressions with powers. Try this: (x+3) (x+6)

• • •                                       x2+3x+6x+18

    •                                                     x2+9x+18                                                                      

    •  If it appears as this, then you've done it correctly.