Question

$$\frac{(2\cdot3)^{3}-(0\cdot3)^{3}}{(2\cdot3)^{2}+(2\cdot3\times0\cdot3)+(0\cdot3)^{2}}$$

Answer

6

Solution


Simplify  \(2\times 3\)  to  \(6\).
\[\frac{{6}^{3}-{(0\times 3)}^{3}}{{6}^{2}+2\times 3\times 0\times 3+{(0\times 3)}^{2}}\]
Simplify  \(0\times 3\)  to  \(0\).
\[\frac{{6}^{3}-{0}^{3}}{{6}^{2}+2\times 3\times 0\times 3+{0}^{2}}\]
Simplify  \({6}^{3}\)  to  \(216\).
\[\frac{216-{0}^{3}}{{6}^{2}+2\times 3\times 0\times 3+{0}^{2}}\]
Simplify  \({0}^{3}\)  to  \(0\).
\[\frac{216-0}{{6}^{2}+2\times 3\times 0\times 3+{0}^{2}}\]
Simplify  \(216-0\)  to  \(216\).
\[\frac{216}{{6}^{2}+2\times 3\times 0\times 3+{0}^{2}}\]
Simplify  \({6}^{2}\)  to  \(36\).
\[\frac{216}{36+2\times 3\times 0\times 3+{0}^{2}}\]
Simplify  \({0}^{2}\)  to  \(0\).
\[\frac{216}{36+2\times 3\times 0\times 3+0}\]
Simplify  \(2\times 3\times 0\times 3\)  to  \(0\).
\[\frac{216}{36+0+0}\]
Simplify  \(36+0\)  to  \(36\).
\[\frac{216}{36+0}\]
Simplify  \(36+0\)  to  \(36\).
\[\frac{216}{36}\]
Simplify.
\[6\]