Question

Find the following product: \[\frac{4}{3}a( a^2 + b^2 - 3 c^2 )\]

Answer 1

To find the product, we will use distributive law as follows:

\[\frac{4}{3}a\left( a^2 + b^2 - 3 c^2 \right)\]

\[ = \frac{4}{3}a \times a^2 + \frac{4}{3}a \times b^2 - \frac{4}{3}a \times 3 c^2 \]

\[ = \frac{4}{3} a^{1 + 2} + \frac{4}{3}a b^2 - 4a c^2 \]

\[ = \frac{4}{3} a^3 + \frac{4}{3}a b^2 - 4a c^2\]

Thus, the answer is \[\frac{4}{3} a^3 + \frac{4}{3}a b^2 - 4a c^2\].