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Algebraic manipulation

Multiplying and dividing algebraic expressions

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Explainer Video

Tutor: Meera

Summary

Multiplying and dividing algebraic expressions

In a nutshell

Algebraic terms can be multiplied or divided, using laws of indices. Numbers can be multiplied or divided as usual.

Multiplying

To multiply two terms, multiply numbers as normal and add the powers on the (same) variables using the rule:

$x^a \times x^b = x^{a+b}$

Examples

$\begin {aligned}a \times 0 &= 0 \\a \times 1 &= a \\a \times a &= a^2 \\a^2 \times a^3 &= a^5 \\2a^4 \times 3a^5 &= 6a^9 \\\end {aligned}$

Dividing

To divide two terms, divide the numbers as normal and subtract the powers on the (same) variables using the rule:

$x^a \div x^b = x^{a-b}$

Examples

$\begin {aligned}\frac {6a} 3 &= 2a \\ \\ \frac {12x} {2x} &= 6 \\ \\ \frac {15x^2} {3x} &= 5x\end {aligned}$

Learn with Basics

Length:

Unit 1

Algebraic notation

Unit 2

Simplifying algebraic expressions

Jump Ahead

Optional

Unit 3

Multiplying and dividing algebraic expressions

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do you multiply or divide terms which have a combination of numbers and letters?

To multiply or divide algebraic terms, multiply or divide the numbers as normal and multiply or divide the variables by using the laws of indices.

How do you divide algrabraic expressions?

To divide algebraic expressions, use laws of indices. a^m / a^n = a^(m-n), so when dividing subtract the powers. For example, a^5 / a^2 = a^3.

How do you multiply algebraic expressions?

To multiply algebraic expressions, use the laws of indices if the variables are the same. The rule is a^m x a^n = a^(m+n), so when multiplying two terms, add the powers. For example, a^2 x a^3 = a^5.

Multiplying

To multiply two terms, multiply numbers as normal and add the powers on the (same) variables using the rule:

x^a \times x^b = x^{a+b}

Examples

\begin {aligned}a \times 0 &= 0 \\a \times 1 &= a \\a \times a &= a^2 \\a^2 \times a^3 &= a^5 \\2a^4 \times 3a^5 &= 6a^9 \\\end {aligned}

Dividing

To divide two terms, divide the numbers as normal and subtract the powers on the (same) variables using the rule:

x^a \div x^b = x^{a-b}

Examples

\begin {aligned}\frac {6a} 3 &= 2a \\ \\ \frac {12x} {2x} &= 6 \\ \\ \frac {15x^2} {3x} &= 5x\end {aligned}

FAQs - Frequently Asked Questions

How do you multiply or divide terms which have a combination of numbers and letters?

To multiply or divide algebraic terms, multiply or divide the numbers as normal and multiply or divide the variables by using the laws of indices.

How do you divide algrabraic expressions?

To divide algebraic expressions, use laws of indices. a^m / a^n = a^(m-n), so when dividing subtract the powers. For example, a^5 / a^2 = a^3.

How do you multiply algebraic expressions?

To multiply algebraic expressions, use the laws of indices if the variables are the same. The rule is a^m x a^n = a^(m+n), so when multiplying two terms, add the powers. For example, a^2 x a^3 = a^5.

Multiplying and dividing algebraic expressions

Videos

Summary

Exercises

Select Lesson

Statistics

Probability

Trigonometry

Drawing shapes

Lines and angles

Measures

Properties of shapes

Shapes

Rates of change

Proportion

Ratio

Other graphs

Straight line graphs

Formulae and equations

Algebraic manipulation

Fractions, decimals and percentages

Number calculations

Types of numbers

Explainer Video

Summary

Multiplying and dividing algebraic expressions

​​In a nutshell

Multiplying

Examples

Dividing

Examples

Learn with Basics

Unit 1

Algebraic notation

Unit 2

Simplifying algebraic expressions

Jump Ahead

Unit 3

Multiplying and dividing algebraic expressions

Final Test

FAQs - Frequently Asked Questions

How do you multiply or divide terms which have a combination of numbers and letters?

How do you divide algrabraic expressions?

How do you multiply algebraic expressions?

Multiplying and dividing algebraic expressions

Videos

Summary

Exercises

Select Lesson

Statistics

Probability

Trigonometry

Drawing shapes

Lines and angles

Measures

Properties of shapes

Shapes

Rates of change

Proportion

Ratio

Other graphs

Straight line graphs

Formulae and equations

Algebraic manipulation

Fractions, decimals and percentages

Number calculations

Types of numbers

Explainer Video

Summary

Multiplying and dividing algebraic expressions

​​In a nutshell

Multiplying

Examples

Dividing

Examples

Learn with Basics

Unit 1

Algebraic notation

Unit 2

Simplifying algebraic expressions

In a nutshell

In a nutshell