Question

Find the product.

(8m^2 – 1)(8m^2 + 1)

a. 64m^2 – 1

b. 64m^4 – 1

c. 64m^4 + 1

d. 64m^3 – 1

Answer 1

Can you multiply binomials using FOIL?

Answer 2

nope

Answer 3

I'll show you. When you need to multiply two binomials, such as your problem, you can use the word FOIL as a reminder of how to do it.

Answer 4

You need to multiply both terms of the first binomial by both terms of the second binomial. To make sure you remember to do every multiplication, follow the letters of the word FOIL with these meanings:
(F)irst
(O)utside
(I)nside
(L)ast

Answer 5

\( (8m^2 - 1)(8m^2 + 1) \)

F: first term times first term
\( (\color{red}{8m^2} - 1)(\color{red}{8m^2} + 1) \)
\(= \color{red}{64m^4} \)

O: outside terms
\( (\color{red}{8m^2} - 1)(8m^2 + \color{red}{1}) \)
\(= 64m^4 \color{red}{+ 8m^2} \)

I: inside terms
\( (8m^2 - \color{red}{1})(\color{red}{8m^2} + 1) \)
\(= 64m^4 + 8m^2 \color{red}{-8m^2} \)

L: last terms
\( (8m^2 - \color{red}{1})(8m^2 + \color{red}{1}) \)
\(= 64m^4 + 8m^2 -8m^2 \color{red} {- 1} \)

Now you have these four terms. Thew two middle terms are like terms and can be combined.
\(= 64m^4 + \color{red} {8m^2 -8m^2} - 1 \)
\(= 64m^4 - 1 \)

Answer 6

That is the way to multiply any two binomials together.

Here's the shortcut for this case.
The middle terms cancelled out leaving only two terms in the answer.
If you have a product of two binomials of the form
\( (a + b)(a - b)\), then the answer is
\( a^2 - b^2 \)

If the two binomials are a sum and a difference of the same two terms, then all you need to do to multiply them together is square the first term, square the second term, and write a minus sign between them.