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Chapter overview
Learning goals
Learning Goals
Maths
Summary
Algebraic terms can be multiplied or divided. If the variables are the same, the laws of indices can be used. When multiplying, different variables can be written together without the mulitplication sign between them. For dividing, variables can be written as a fraction. Numbers can be multiplied or divided as usual.
To multiply two terms, multiply numbers as normal and add the powers on the (same) variables using the rule:
$x^a \times x^b = x^{a+b}$
This rule can only be applied if variables are the same. If variables are different, write them together, omitting the multiplication sign. The number on the power tells you how many times that variable has been multiplied together.
$\begin {aligned}a \times 0 &= 0 \\a \times 1 &= a \\a \times a &= a^2 \\a^2 \times a^3 &= a^5 \\2a^4 \times 3a^5 &= 6a^9 \\ a \times b &= ab \\ 2a^2 \times 5ab &=10a^3b \\\end {aligned}$
To divide two terms, divide the numbers as normal and subtract the powers on the (same) variables using the rule:
$x^a \div x^b = x^{a-b}$
This rule can only be applied if the variables are the same. If the variables are different, write them as a fraction.
$\begin {aligned}\frac {6a} 3 &= 2a \\\frac {12x} {2x} &= 6 \\\frac {15x^2} {3x} &= 5x \\ \frac {10a} {2b} &= \frac {5a} b \\ \frac {27a^3b^2c} {3a^2c} &= 9ab^2\end {aligned}$
Algebraic terms can be multiplied or divided. If the variables are the same, the laws of indices can be used. When multiplying, different variables can be written together without the mulitplication sign between them. For dividing, variables can be written as a fraction. Numbers can be multiplied or divided as usual.
To multiply two terms, multiply numbers as normal and add the powers on the (same) variables using the rule:
$x^a \times x^b = x^{a+b}$
This rule can only be applied if variables are the same. If variables are different, write them together, omitting the multiplication sign. The number on the power tells you how many times that variable has been multiplied together.
$\begin {aligned}a \times 0 &= 0 \\a \times 1 &= a \\a \times a &= a^2 \\a^2 \times a^3 &= a^5 \\2a^4 \times 3a^5 &= 6a^9 \\ a \times b &= ab \\ 2a^2 \times 5ab &=10a^3b \\\end {aligned}$
To divide two terms, divide the numbers as normal and subtract the powers on the (same) variables using the rule:
$x^a \div x^b = x^{a-b}$
This rule can only be applied if the variables are the same. If the variables are different, write them as a fraction.
$\begin {aligned}\frac {6a} 3 &= 2a \\\frac {12x} {2x} &= 6 \\\frac {15x^2} {3x} &= 5x \\ \frac {10a} {2b} &= \frac {5a} b \\ \frac {27a^3b^2c} {3a^2c} &= 9ab^2\end {aligned}$
Multiplying and dividing algebraic expressions
FAQs
Question: How do you multiply or divide variables with different letters in algebra?
Answer: When multiplying variables with different letters, the variables can be written together without the mulitplication sign between them, for example, 2x x 3y = 6xy. For dividing variables with different letters, variables can be written as a fraction, for example, 6x / 2y = 3x/y.
Question: How do you divide algrabraic expressions?
Answer: To divide algebraic expressions, use the laws of indices if the variables are the same. The rule is a^m / a^n = a^(m-n), when you are dividing, subtract the powers. E.g. a^5 / a^2 = a^3.
Question: How do you multiply algebraic expressions?
Answer: 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.
Theory
Exercises
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