Sure! Let's multiply the binomials [tex]\((x - 1)(8x - 4)\)[/tex] using the FOIL method and then combine like terms.
FOIL stands for First, Outer, Inner, Last. We multiply each of these pairs and then add the results together:
1. First: Multiply the first terms in each binomial:
[tex]\[
x \cdot 8x = 8x^2
\][/tex]
2. Outer: Multiply the outer terms in each binomial:
[tex]\[
x \cdot -4 = -4x
\][/tex]
3. Inner: Multiply the inner terms in each binomial:
[tex]\[
-1 \cdot 8x = -8x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
-1 \cdot -4 = 4
\][/tex]
Now, combine all the products we found:
[tex]\[
8x^2 - 4x - 8x + 4
\][/tex]
Next, we combine the like terms [tex]\(-4x\)[/tex] and [tex]\(-8x\)[/tex]:
[tex]\[
8x^2 - 4x - 8x + 4 = 8x^2 - 12x + 4
\][/tex]
So, the product of the binomials [tex]\((x - 1)(8x - 4)\)[/tex] is:
[tex]\[
8x^2 - 12x + 4
\][/tex]
