#### Example 1

Write each of the following using concise algebraic notation.

- A number x is multiplied by itself and then doubled.
- A number x is squared and then multiplied by the square of a second number y.
- A number x is multiplied by a number y and the result is squared.

#### Solution

- \(x × x × 2 = x^2 × 2 = 2x^2\)
- \(x^2 × y^2 = x^2y^2\)
- \((x × y)^2 = (xy)^2\) which is equal to \(x^2y^2\)

#### Summary

\(2 × x\) is written as 2\(x\) | \(x^1 = x\) (the first power of \(x\) is \(x\)) |

\(x × y\) is written as \(xy\) or \(yx\) | \(x^0 = 1 (x \neq 0)\) |

\(x × y × z\) is written as \(xyz\) | \(1x = x\) |

\(x × x\) is written as \(x^2\) | \(0x = 0\) |

\(4 × x × x × x = 4x^3\) | |

\(x ÷ 3\) is written as \(\dfrac{x}{3}\) | |

\(x ÷ (yz)\) is written as \(\dfrac{x}{yz}\) |