To find the product [tex]\((p + 5)(p - 2)\)[/tex], we need to use the distributive property, also known as the FOIL method (First, Outer, Inner, Last):
1. First: Multiply the first terms in each binomial:
[tex]\( p \cdot p = p^2 \)[/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\( p \cdot (-2) = -2p \)[/tex]
3. Inner: Multiply the inner terms in the binomials:
[tex]\( 5 \cdot p = 5p \)[/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\( 5 \cdot (-2) = -10 \)[/tex]
Next, add up all these products to get the expanded form:
[tex]\[ p^2 + (-2p) + 5p + (-10) \][/tex]
Combine the like terms:
[tex]\[ p^2 + 3p - 10 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{p^2 + 3p - 10} \][/tex]
So, the correct choice is:
A. [tex]\(p^2 + 3p - 10\)[/tex]
