Factor Algebraic Expressions Containing Fractional and Negative Exponents
-$$( x + 6 ) ^ { 2 / 5 } - ( x + 6 ) ^ { 12 / 5 }$$

Question

Quizplus · Accepted Answer

The expression can be factored by taking out the common factor $(x + 6)^{2/5}$, resulting in $(x + 6)^{2/5}(1 - (x + 6)^{10/5})$, which simplifies to $(x + 6)^{2/5}(1 - (x + 6)^2)$. Expanding $(x + 6)^2$ gives $x^2 + 12x + 36$, and subtracting this from 1 gives the expression in choice A: $(x + 6)^{2/5}(-x^2 - 12x - 35)$.

Factor Algebraic Expressions Containing Fractional and Negative Exponents - (x+6)2/5−(x+6)12/5( x + 6 ) ^ { 2 / 5 } - ( x + 6 ) ^ { 12 / 5 }(x+6)2/5−(x+6)12/5

Factor Algebraic Expressions Containing Fractional and Negative Exponents
- $( x + 6 ) ^ { 2 / 5 } - ( x + 6 ) ^ { 12 / 5 }$