FOIL stands for First, Outside, Inside, Last. It is an algorithm used for multiplying binomials.

(3a + b)(-2a - 4b)

Product of the **First** terms: 3a * -2a = -6a^2

Product of the **Outside** terms: 3a * -4b = -12ab

Product of the **Inside** terms: b * -2a = -2ab

Product of the **Last** terms: b * -4b = -4b^2

-6a^2 + -12ab + -2ab + -4b^2

Add like terms.

**-6a^2 + -14ab + -4b^2**

or

**-6a^2 - 14ab - 4b^2**

We have to determine the result of (3a+b)(-2a-4b).

Using FOIL, first multiply the first terms, or 3a and -2a, then multiply the outer terms or 3a and -4b, then multiply the inner terms b and -2a and finally multiply the last terms b and -4b.

(3a+b)(-2a-4b)

=> 3a*(-2a) + 3a*(-4b) + b*(-2a) + b*(-4b)

=> -6a^2 - 12ab - 2ab - 4b^2

=> -6a^2 - 14ab - 4b^2

**The result of (3a+b)(-2a-4b) = -6a^2 - 14ab - 4b^2**

FOIL mean First Outer Inner Last

(3a+b)(-2a-4b)

Think of this as:

`3a*(-2a) + 3a*(-4b) + b*(-2a) + b*(-4b)`

`-6a^2 - 12ab - 2ab - 4b^2`

Combine terms, this leaves:

`-6a^2 - 14ab - 4b^2`

(3a+b)(-2a-4b)

To with FOIL-FIRST, OUTSIDE, INSIDE, LAST

- Rewrite (3a+b)(-2a-4b)
- Use Foil (3a)(-2a)+(3a)(-4b)+(-2a)(b)+(b)(-4b)
- Simplify `-6a^(2)-12ab-2ab-4b^(2)`
- Combine like terms: `-6a^(2)-14ab-4b^(2)`

(3a+b)(-2a-4b)

Distribute the 3a to the -2a and -4b and you will get -6a^2-12ab

Then you distribute the b to the -2a and -4b and you will get -2ab - 4b^2

and then you combine like terms and you will get

-6a^2 - 4b^2 - 14ab