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Marysya12 [62]
2 years ago
6

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

Mathematics
1 answer:
4vir4ik [10]2 years ago
7 0

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}}

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