#### 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 $$\dfrac{x}{yz}$$