To multiply and simplify the expression [tex]\((4r - 1)(5r + 3)\)[/tex], we use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Here's a detailed, step-by-step solution:
1. First Terms: Multiply the first terms in each binomial:
[tex]\[
4r \cdot 5r = 20r^2
\][/tex]
2. Outer Terms: Multiply the outer terms in the binomials:
[tex]\[
4r \cdot 3 = 12r
\][/tex]
3. Inner Terms: Multiply the inner terms in the binomials:
[tex]\[
-1 \cdot 5r = -5r
\][/tex]
4. Last Terms: Multiply the last terms in each binomial:
[tex]\[
-1 \cdot 3 = -3
\][/tex]
Now, we combine all these results together:
[tex]\[
20r^2 + 12r - 5r - 3
\][/tex]
5. Combine like terms: Simplify by combining the like terms ([tex]\(12r\)[/tex] and [tex]\(-5r\)[/tex]):
[tex]\[
20r^2 + (12r - 5r) - 3 = 20r^2 + 7r - 3
\][/tex]
Therefore, the simplified form of the given expression [tex]\((4r - 1)(5r + 3)\)[/tex] is:
[tex]\[
20r^2 + 7r - 3
\][/tex]
