Example 1

Write each of the following using concise algebraic notation.

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

Solution

1. \(x × x × 2 = x^2 × 2 = 2x^2\)
2. \(x^2 × y^2 = x^2y^2\)
3. \((x × y)^2 = (xy)^2\) 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 \(\dfrac{x}{yz}\)