Sure, let's expand and simplify the expression [tex]\((x-5)(4x+11)\)[/tex].
1. Distribute each term in the first parenthesis to every term in the second parenthesis. This means we will multiply [tex]\(x\)[/tex] by each term in [tex]\(4x + 11\)[/tex] and then [tex]\(-5\)[/tex] by each term in [tex]\(4x + 11\)[/tex].
2. First, distribute [tex]\(x\)[/tex]:
[tex]\[
x \cdot 4x = 4x^2
\][/tex]
[tex]\[
x \cdot 11 = 11x
\][/tex]
3. Next, distribute [tex]\(-5\)[/tex]:
[tex]\[
-5 \cdot 4x = -20x
\][/tex]
[tex]\[
-5 \cdot 11 = -55
\][/tex]
4. Combine all of these results:
[tex]\[
4x^2 + 11x - 20x - 55
\][/tex]
5. Simplify by combining like terms ([tex]\(11x\)[/tex] and [tex]\(-20x\)[/tex]):
[tex]\[
4x^2 + (11x - 20x) - 55
\][/tex]
[tex]\[
4x^2 - 9x - 55
\][/tex]
So, the expanded and simplified form of [tex]\((x-5)(4x+11)\)[/tex] is:
[tex]\[
4x^2 - 9x - 55
\][/tex]
