Question

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

Answer 1

Answer:

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

Step-by-step explanation:

$\textsf{Given expression}:$

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

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

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

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

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

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

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

$\textsf{Simplify}:$

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

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

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