To simplify the expression \((x + 2)(2x + 5)\), we can use the distributive property (also known as the FOIL method for binomials). The steps are as follows:
1. First, multiply the first terms in each binomial:
[tex]\[
x \cdot 2x = 2x^2
\][/tex]
2. Outer, multiply the outer terms:
[tex]\[
x \cdot 5 = 5x
\][/tex]
3. Inner, multiply the inner terms:
[tex]\[
2 \cdot 2x = 4x
\][/tex]
4. Last, multiply the last terms:
[tex]\[
2 \cdot 5 = 10
\][/tex]
Next, combine all these products:
[tex]\[
2x^2 + 5x + 4x + 10
\][/tex]
Now, combine the like terms \(5x\) and \(4x\):
[tex]\[
2x^2 + 9x + 10
\][/tex]
Thus, the simplified expression is:
[tex]\[
2x^2 + 9x + 10
\][/tex]
Therefore, the coefficients for the simplified expression \(2x^2 + 9x + 10\) are:
[tex]\[
\boxed{2}
\][/tex]
[tex]\[
\boxed{9}
\][/tex]
[tex]\[
\boxed{10}
\][/tex]
