In algebra, to multiply two binomials, a method is defined called as |

When we multiply two binomials, we will get four terms:

**First:**Multiply the first terms of both binomials.**Outside:**Multiply first term of first binomial with last term of second binomial.**Inner:**Multiply last term of first binomial and first term of second binomial.**Last:**Multiply last terms of both the binomials.

Reverse foil method is a process of doing foil backward. It is used to write the information in a more organized way and helps us to understand how FOIL works, when multiplying two binomials.

Reverse foil method of factoring trinomials is in the form x$^{2}$ + bx + c. Through this method, we can convert the trinomial back into a double binomial expression.

Steps to be considered are given below :

- Set two sets of parentheses for trinomial equation like (_ $\pm$ _) (_ $\pm$ _).
- Factor the given polynomial.
- Find the possible factors of the last term.
- Plug in the obtained number groups in the given equation. Check whether the obtained factors hold true or not in the given equation.
- Keep plugging the factors and check it with the FOIL. If the factors hold true in the given equation, then you've got the answer.

Polynomial equation also known as algebraic equation is of the form $a_{n}x^{n}$ + $a_{n-1}x^{n-1}$ + .......+ $a_{1}$x + $a_{0}$ = 0

### Solved Example

**Question:**Solve (2x + 5) (x$^{3}$ + 10x$^{2}$ + 8x + 3).

**Solution:**

The second expression can be split as (x$^{3}$ + 10x$^{2}$) + (8x + 3), so that, we can apply FOIL.

It can be solved now as follows:

(2x + 5)( (x$^{3}$ + 10x$^{2}$) + (2x + 5) (8x + 3) (Use FOIL again)

= 2x(x$^{3}$) + 2x(10x$^{2}$) + 5x$^{3}$ + 50x$^{2}$ + 2x(8x) + 2x(3) + 5(8x) + 5(3)

= 2x$^{4}$ + 25x$^{3}$ + 66x$^{2}$ + 46x + 15

### Solved Example

**Question:**Solve (5x - 2) (5x$^{2}$ + 7x - 5)

**Solution:**

= 25x$^{3}$ + 35x$^{2}$ - 25x - 10x$^{2}$ - 14x + 10

= 25x$^{3}$ + 25x$^{2}$ - 39x + 10

### Solved Examples

**Question 1:**Multiply (5x - 4) (x - 4) using FOIL method.

**Solution:**

**First:**$5x \times x = 5x^{2}$

**Outside:**$5x \times (-4) = -20x$

**Inside:**$- 4 \times x = -4x$

**Last:**$(-4) \times (-4) = 16$

Summing it all up, we get the trinomial equation as $5x^{2} - 24x + 16$

**Question 2:**Solve x$^{2}$ + 13x + 36 using reverse FOIL method.

**Solution:**

**Step 1:**

Set two sets of parentheses for trinomial equation like: (_ $\pm$ _) (_ $\pm$ _).

Coefficient of first term is 1. So, the binomials of the first terms are x and x.

So, we have, (x $\pm$ _) (x $\pm$ _).

**Step 2:**

Factor the given polynomial.

As the last sign is positive, find the factors of 36 that add to give 13.

**Step 3:**

Possible factors of the last term '36' are (1, 36), (2, 18), (3, 12), (4, 9), (6, 6)

**Step 4:**

As 4 and 9 only add to give 13. These factors are the last numbers in the binomial factors as the other factors doesn't hold true for the given equation

**(x + 4) (x + 9)**.