Question
Find the product:
$\frac{4}{3}\text{a}\big(\text{a}^2 +\text{ b}^2 − 3\text{c}^2\big)$
$\frac{4}{3}\text{a}\big(\text{a}^2 +\text{ b}^2 − 3\text{c}^2\big)$
✓
Answer
To find the product, we will use distributive law as follows:$\frac{4}{3}\text{a}\big(\text{a}^2 +\text{ b}^2 − 3\text{c}^2\big)$
$=\frac{4}{3}\text{a}×\text{a}^2+\frac{4}{3}\text{a}×\text{b}^2−\frac{4}{3}\text{a}×3\text{c}^2$
$=\frac{4}{3}\text{a}^{1+2}+\frac{4}{3}\text{ab}^2−4\text{ac}^2$
$=\frac{4}{3}\text{a}^3+\frac{4}{3}\text{ab}^2−4\text{ac}^2$
Thus, the answer is $\frac{4}{3}\text{a}^3+\frac{4}{3}\text{ab}^2−4\text{ac}^2$
$=\frac{4}{3}\text{a}×\text{a}^2+\frac{4}{3}\text{a}×\text{b}^2−\frac{4}{3}\text{a}×3\text{c}^2$
$=\frac{4}{3}\text{a}^{1+2}+\frac{4}{3}\text{ab}^2−4\text{ac}^2$
$=\frac{4}{3}\text{a}^3+\frac{4}{3}\text{ab}^2−4\text{ac}^2$
Thus, the answer is $\frac{4}{3}\text{a}^3+\frac{4}{3}\text{ab}^2−4\text{ac}^2$
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