To solve the expression [tex]\(\left(y^2 + y\right)\left(3y^3 - 2y^3\right)\)[/tex] and determine what property it exemplifies, let's break it down step by step.
1. Simplify the inner expression:
[tex]\[
3y^3 - 2y^3 = y^3
\][/tex]
2. Substitute back into the original expression:
[tex]\[
(y^2 + y)(y^3)
\][/tex]
3. Apply the distributive property:
We need to distribute [tex]\(y^3\)[/tex] to both [tex]\(y^2\)[/tex] and [tex]\(y\)[/tex] in the binomial [tex]\(y^2 + y\)[/tex]:
[tex]\[
(y^2 \cdot y^3) + (y \cdot y^3)
\][/tex]
4. Combine the exponents:
[tex]\[
y^{2+3} + y^{1+3} = y^5 + y^4
\][/tex]
From this process, we can clearly see that the steps involve distributing the [tex]\(y^3\)[/tex] across the terms in [tex]\(y^2 + y\)[/tex]. This is an explicit use of the distributive property.
Therefore, the correct answer is:
C. The distributive property
