Multiplying and Dividing Terms

In short: To multiply terms, multiply the numbers and then write the letters, so $3x\times 2y=6xy$ and $x\times x=x^2$. To divide, write it as a fraction and cancel what is the same on the top and bottom.

Before you start

• No sign between a number and a letter means multiply: $4a=4\times a$.
• Powers: $a^3=a\times a\times a$.
• Simplifying fractions by dividing top and bottom by the same number: $\frac{6}{9}=\frac{2}{3}$.
• Multiplying can be done in any order: $2\times 7\times 5=2\times 5\times 7=70$.

Multiplying terms

Any terms can be multiplied, like or unlike. $3x\times 2y=6xy$ is fine.

Index notation

When the same letter is multiplied by itself, write it with a power.

$$x\times x\times x=x^3$$

$$x\times x\times 3y=3x^{2}y$$

$$3\times p\times p\times 5=15p^2$$

Dividing terms

A division can be written as a fraction. Then cancel anything that is on both the top and the bottom.

Quick summary

• To multiply terms, multiply the numbers, then write the letters.
• Unlike terms can be multiplied: $3x\times 2y=6xy$.
• Repeated letters use powers: $x\times x=x^2$.
• When multiplying the same letter, add the powers: $a^2\times a^3=a^5$.
• To divide, write a fraction and cancel what is on top and bottom.
• When the top is a sum, divide every term.

Quiz