To multiply and simplify the expression [tex]\((5b - 2)(2b + 1)\)[/tex], we'll use the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last).
1. First: Multiply the first terms in each binomial:
[tex]\[
(5b) \times (2b) = 10b^2
\][/tex]
2. Outer: Multiply the outer terms in the product:
[tex]\[
(5b) \times 1 = 5b
\][/tex]
3. Inner: Multiply the inner terms in the product:
[tex]\[
(-2) \times (2b) = -4b
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
(-2) \times 1 = -2
\][/tex]
Now, combine all these products together:
[tex]\[
10b^2 + 5b - 4b - 2
\][/tex]
Combine the like terms [tex]\(5b\)[/tex] and [tex]\(-4b\)[/tex]:
[tex]\[
10b^2 + (5b - 4b) - 2 = 10b^2 + 1b - 2
\][/tex]
Therefore, the simplified expression is:
[tex]\[
\boxed{10b^2 + b - 2}
\][/tex]
