Question

Can somebody simplify this?

Answer 1

\[f(\frac{ 2 }{ 3 }a)= (\frac{ 2 }{ 3 }a)^3- a(\frac{ 2}{ 3 }a)^2 \]
where a>0. Solve in terms of a

Answer 2

What is \[(\frac{2}{3}a)^3\]What is \[(\frac{2}{3}a)^2\]

Answer 3

(8a/27) and (4a/9), respectively

Answer 4

ergo, (8a/27)-a*(12a/27)

Answer 5

and then my answer deviates from the book

Answer 6

\[(\frac{2}{3}a)^3 = \frac{2^3}{3^3}a^3 = \frac{8}{27}a^3\]
\[(\frac{2}{3}a)^2 = \frac{2^2}{3^2}a^2 = \frac{4}{9}a^2\]
\[(\frac{2}{3}a)^3 - a(\frac{2}{3}a)^2 = \frac{8}{27}a^3 - a\frac{4}{9}a^2 = \frac{8}{27}a^3-\frac{4}{9}a^3\]\[=\frac{8}{27}a^3-\frac{12}{27}a^3 =-\frac{4}{27}a^3 \]