71.1k views
7 votes
Factor the following expression. Simplify your answer.
5t( -2t + 3)^2/3 +2( -2t + 3)^5/3

1 Answer

4 votes

Answer:


(t+6)(-2t+3)^{(2)/(3)}

Explanation:


\textsf{Given expression}:


5t(-2t+3)^{(2)/(3)}+2(-2t+3)^{(5)/(3)}


\textsf{Apply exponent rule} \quad a^(b+c)=a^b \cdot a^c:


\implies 5t(-2t+3)^{(2)/(3)}+2(-2t+3)^{(3+2)/(3)}


\implies 5t(-2t+3)^{(2)/(3)}+2(-2t+3)^{(3)/(3)}(-2t+3)^{(2)/(3)}


\implies 5t(-2t+3)^{(2)/(3)}+2(-2t+3)(-2t+3)^{(2)/(3)}


\textsf{Factor out common term }(-2t+3)^{(2)/(3)}:


\implies (-2t+3)^{(2)/(3)}(5t+2(-2t+3))


\textsf{Simplify}:


\implies (-2t+3)^{(2)/(3)}(5t-4t+6)


\implies (-2t+3)^{(2)/(3)}(t+6)


\implies (t+6)(-2t+3)^{(2)/(3)}

User Alter
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories