To find the expanded form of the expression [tex]\((3x - 5)(5x + 8)\)[/tex], we will use the distributive property, also known as the FOIL method for binomials. The acronym FOIL stands for First, Outer, Inner, Last, which indicates the terms we need to multiply together.
1. First: Multiply the first terms of each binomial.
[tex]\[
(3x) \cdot (5x) = 15x^2
\][/tex]
2. Outer: Multiply the outer terms of each binomial.
[tex]\[
(3x) \cdot (8) = 24x
\][/tex]
3. Inner: Multiply the inner terms of each binomial.
[tex]\[
(-5) \cdot (5x) = -25x
\][/tex]
4. Last: Multiply the last terms of each binomial.
[tex]\[
(-5) \cdot (8) = -40
\][/tex]
Now, we add all these products together:
[tex]\[
15x^2 + 24x - 25x - 40
\][/tex]
Combine like terms (the [tex]\(x\)[/tex] terms in this case):
[tex]\[
15x^2 + (24x - 25x) - 40
\][/tex]
Simplify the coefficients of [tex]\(x\)[/tex]:
[tex]\[
15x^2 - x - 40
\][/tex]
So, the expanded form of [tex]\((3x - 5)(5x + 8)\)[/tex] is:
[tex]\[
15x^2 - x - 40
\][/tex]
