Sure, I'd be happy to walk you through the process of multiplying and simplifying the expression [tex]\((x-4)(4x+3)\)[/tex].
1. Distribute each term in the first expression to the second expression:
[tex]\[
(x - 4)(4x + 3)
\][/tex]
2. Multiply [tex]\(x\)[/tex] by each term in the second expression:
[tex]\[
x \cdot 4x + x \cdot 3
\][/tex]
This results in:
[tex]\[
4x^2 + 3x
\][/tex]
3. Multiply [tex]\(-4\)[/tex] by each term in the second expression:
[tex]\[
-4 \cdot 4x + -4 \cdot 3
\][/tex]
This results in:
[tex]\[
-16x - 12
\][/tex]
4. Combine all these terms together:
[tex]\[
4x^2 + 3x - 16x - 12
\][/tex]
5. Combine like terms:
[tex]\[
4x^2 + (3x - 16x) - 12
\][/tex]
Simplify the expression inside the parentheses:
[tex]\[
4x^2 - 13x - 12
\][/tex]
So, the simplified result of [tex]\((x-4)(4x+3)\)[/tex] is:
[tex]\[
4x^2 - 13x - 12
\][/tex]
This is the final simplified expression.
