Alright, let's simplify the expression [tex]\((4x - 3)(x + 5)\)[/tex] step by step.
To simplify this expression, we can use the distributive property (also known as the FOIL method for binomials in this case), which stands for First, Outer, Inner, Last.
1. First: Multiply the first terms in each binomial:
[tex]\[
4x \cdot x = 4x^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\[
4x \cdot 5 = 20x
\][/tex]
3. Inner: Multiply the inner terms in the binomials:
[tex]\[
-3 \cdot x = -3x
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
-3 \cdot 5 = -15
\][/tex]
Now, combine all these results:
[tex]\[
4x^2 + 20x - 3x - 15
\][/tex]
Combine the like terms (the terms with [tex]\(x\)[/tex]):
[tex]\[
4x^2 + (20x - 3x) - 15 = 4x^2 + 17x - 15
\][/tex]
So, the simplified form of the expression [tex]\((4x - 3)(x + 5)\)[/tex] is:
[tex]\[
4x^2 + 17x - 15
\][/tex]
Thus, the correct answer is:
C. [tex]\(4x^2 + 17x - 15\)[/tex]
