# How do you FOIL # (x^3 – x^2)(x^3 + x^2)#?

##### 3 Answers

#### Answer:

#### Explanation:

FOIL is a mnemonic to help remember all of the combinations you need to multiply and add when finding the product of two binomials.

In our example, we find:

#(x^3-x^2)(x^3+x^2) = overbrace((x^3)(x^3))^"First"+overbrace((x^3)(x^2))^"Outside"+overbrace((-x^2)(x^3))^"Inside"+overbrace((-x^2)(x^2))^"Last"#

#color(white)((x^3-x^2)(x^3+x^2)) = x^6+color(red)(cancel(color(black)(x^5)))-color(red)(cancel(color(black)(x^5)))-x^4#

#color(white)((x^3-x^2)(x^3+x^2)) = x^6-x^4#

In fact, in this particular example, we might note that the multiplication takes the form

In general, we have:

#(A-B)(A+B) = A^2-B^2#

This is known as the difference of squares identity.

In our particular example:

#(x^3-x^2)(x^3+x^2) = (x^3)^2-(x^2)^2 = x^6-x^4#

#### Answer:

#### Explanation:

FOIL is extremely useful in multiplying binomials. To be able to use it, let's understand what it means first:

**FOIL stands for Firsts, Outsides, Insides, Lasts**, meaning we multiply the first terms, outside terms, inside terms, and last terms, respectively.

In

- Firsts
#(x^3*x^3)= x^6# - Outsides
#(x^3*x^2)= x^5# - Insides
#(-x^2*x^3)= -x^5# - Lasts
#(-x^2*x^2)= -x^4#

Thus, we have:

The middle terms will cancel out (as expected, because the original problem is in the difference of squares format), and we get:

We can factor out an

#### Answer:

the answer is

#### Explanation:

(

=

*_ First *

**Outer****__**

**Inner****Last**

=