Question 1

Factor the following expression. Simplify your answer.
5t( -2t + 3)^2/3 +2( -2t + 3)^5/3

Question 2

Answer:

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

Explanation:

$\textsf{Given expression}:$

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

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

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

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

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

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

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

$\textsf{Simplify}:$

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

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

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

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