Certainly! Let's go through the process of multiplying and simplifying the expression step-by-step.
Given the expression:
[tex]\[
(4x - 1)(6x + 7)
\][/tex]
1. Distribute each term in the first binomial to each term in the second binomial:
Using the distributive property (also known as the FOIL method for binomials), we multiply each term in [tex]\( (4x - 1) \)[/tex] by each term in [tex]\( (6x + 7) \)[/tex].
[tex]\[
(4x - 1)(6x + 7) = 4x \cdot 6x + 4x \cdot 7 - 1 \cdot 6x - 1 \cdot 7
\][/tex]
2. Perform the multiplications:
[tex]\[
4x \cdot 6x = 24x^2
\][/tex]
[tex]\[
4x \cdot 7 = 28x
\][/tex]
[tex]\[
-1 \cdot 6x = -6x
\][/tex]
[tex]\[
-1 \cdot 7 = -7
\][/tex]
3. Combine the results:
[tex]\[
24x^2 + 28x - 6x - 7
\][/tex]
4. Combine like terms ([tex]\(28x\)[/tex] and [tex]\(-6x\)[/tex]):
[tex]\[
28x - 6x = 22x
\][/tex]
So, the simplified expression is:
[tex]\[
24x^2 + 22x - 7
\][/tex]
Thus, the product of [tex]\((4x - 1)\)[/tex] and [tex]\((6x + 7)\)[/tex] is:
[tex]\[
24x^2 + 22x - 7
\][/tex]
