To simplify the expression [tex]\(4.5p(2 - 0.2p)\)[/tex], follow these steps:
1. Apply the distributive property: The distributive property states that [tex]\(a(b + c) = ab + ac\)[/tex]. Here, [tex]\(a = 4.5p\)[/tex], [tex]\(b = 2\)[/tex], and [tex]\(c = -0.2p\)[/tex].
2. Distribute [tex]\(4.5p\)[/tex] through the parenthesis:
[tex]\[
4.5p(2 - 0.2p) = 4.5p \cdot 2 + 4.5p \cdot (-0.2p)
\][/tex]
3. Perform the individual multiplications:
- For the first term, [tex]\(4.5p \cdot 2\)[/tex]:
[tex]\[
4.5p \cdot 2 = 9p
\][/tex]
- For the second term, [tex]\(4.5p \cdot (-0.2p)\)[/tex]:
[tex]\[
4.5p \cdot (-0.2p) = -0.9p^2
\][/tex]
4. Combine the simplified terms:
[tex]\[
9p - 0.9p^2
\][/tex]
Thus, the simplified form of [tex]\(4.5p(2 - 0.2p)\)[/tex] is:
[tex]\[
9p - 0.9p^2
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{9p - 0.9p^2}
\][/tex]
