To square the given binomial [tex]\((4x - 3)^2\)[/tex], let's go through the steps carefully:
1. Express the binomial squared:
[tex]\[
(4x - 3)^2
\][/tex]
2. Use the formula for squaring a binomial:
[tex]\[
(a - b)^2 = a^2 - 2ab + b^2
\][/tex]
Here, [tex]\(a = 4x\)[/tex] and [tex]\(b = 3\)[/tex].
3. Apply the formula to our binomial:
[tex]\[
(4x - 3)^2 = (4x)^2 - 2 \cdot (4x) \cdot (3) + (3)^2
\][/tex]
4. Calculate each part separately:
- [tex]\((4x)^2 = 16x^2\)[/tex]
- [tex]\(-2 \cdot (4x) \cdot (3) = -24x\)[/tex]
- [tex]\((3)^2 = 9\)[/tex]
5. Combine all parts together:
[tex]\[
(4x - 3)^2 = 16x^2 - 24x + 9
\][/tex]
So, after expanding [tex]\((4x - 3)^2\)[/tex], we get:
[tex]\[
16x^2 - 24x + 9
\][/tex]
The coefficient of the [tex]\(x\)[/tex] term in this expanded expression is [tex]\(-24\)[/tex].
Therefore, the coefficient of the [tex]\(x\)[/tex] term in the result is:
[tex]\[
-24
\][/tex]
The complete solution, written as required, is:
[tex]\[
(16x^2 - 24x + 9)
\][/tex]
To summarize, the coefficient of the [tex]\(x\)[/tex] term in the result is [tex]\(-24\)[/tex]
