Question

$$81 { x }^{ 2 } -2 \times 81x \times 10 { x }^{ 2 } { y }^{ 3 }$$

Answer

$$81*x^2-1620*x^3*y^3$$

Solution


Take out the constants.
\[81{x}^{2}-(2\times 81\times 10)x{x}^{2}{y}^{3}\]
Simplify  \(2\times 81\)  to  \(162\).
\[81{x}^{2}-(162\times 10)x{x}^{2}{y}^{3}\]
Simplify  \(162\times 10\)  to  \(1620\).
\[81{x}^{2}-1620x{x}^{2}{y}^{3}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[81{x}^{2}-1620{x}^{1+2}{y}^{3}\]
Simplify  \(1+2\)  to  \(3\).
\[81{x}^{2}-1620{x}^{3}{y}^{3}\]