Question

Pls Halp...

Rewrite the expression as a sum of terms, where each term is in the form k*a^n.


sqrt( a ) ( 2a^2 - 4/a )

Answer 1

The expression as a sum of terms is
`2\cdot a^{(3)/(2) } - 4\cdot a^{-(1)/(2) }`.

Explanation:

The expression to be rewritten has the following form:

`√(a) \cdot (2\cdot a^(2)-(4)/(a) )`

A polynomial as a sum of terms consists in a sum of terms of the form
`c_(i) \cdot a^(k(i))`, where
`c_(i)` and
`k_(i)` are the i-th coefficient and exponent. The expression has to be expanded to create the sum of terms:

`a^{(1)/(2) }\cdot (2\cdot a^(2) - 4\cdot a^(-1))`

`2\cdot a^{1 + (1)/(2) } - 4\cdot a^{-1+(1)/(2) }`

`2\cdot a^{(3)/(2) } - 4\cdot a^{-(1)/(2) }`

The expression as a sum of terms is
`2\cdot a^{(3)/(2) } - 4\cdot a^{-(1)/(2) }`.