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Multiplying and dividing algebraic expressions

Multiplying and dividing algebraic expressions

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Proportion


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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: 

xa×xb=xa+bx^a \times x^b = x^{a+b}​​
​​

Examples

a×0=0a×1=aa×a=a2a2×a3=a52a4×3a5=6a9\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:

 xa÷xb=xabx^a \div x^b = x^{a-b}


Examples

6a3=2a12x2x=615x23x=5x\begin {aligned}\frac {6a} 3 &= 2a \\ \\ \frac {12x} {2x} &= 6 \\ \\ \frac {15x^2} {3x} &= 5x\end {aligned}


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Exercises

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?

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