To simplify the expression [tex]\( 3(p^2 + q^2) - 3q(p^2 + q^2) \)[/tex], let's break it down step-by-step:
1. Distribute the 3 in the first term:
[tex]\[
3(p^2 + q^2) \rightarrow 3p^2 + 3q^2
\][/tex]
2. Distribute the [tex]\(-3q\)[/tex] in the second term:
[tex]\[
-3q(p^2 + q^2) \rightarrow -3q \cdot p^2 - 3q \cdot q^2 \rightarrow -3qp^2 - 3q^3
\][/tex]
3. Now, combine the simplified expressions from steps 1 and 2:
[tex]\[
(3p^2 + 3q^2) - (3qp^2 + 3q^3)
\][/tex]
4. Combine like terms (if any):
- We see that there are no like terms involving [tex]\( 3p^2 \)[/tex] and [tex]\( -3qp^2 \)[/tex] or [tex]\( 3q^2 \)[/tex] and [tex]\( -3q^3 \)[/tex].
5. Thus, the simplified expression is:
[tex]\[
3p^2 + 3q^2 - 3qp^2 - 3q^3
\][/tex]
So, the simplified form of the expression [tex]\( 3(p^2 + q^2) - 3q(p^2 + q^2) \)[/tex] is:
[tex]\[
3p^2 + 3q^2 - 3qp^2 - 3q^3
\][/tex]
