Simplifying Expressions with Multiple Variables
Simplifying expressions with multiple variables means writing them in their shortest form. You collect like terms with the same letters, so 2a + 3b + 5a - b becomes 7a + 2b. You also use exponents, writing x × y × y as xy².
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Expressions with Multiple Variables
- An expression has multiple variables if it has more than one letter.
- For example, has the variables a, b, and c.
Using Exponents to Simplify
- Exponents are used for repeated multiplication.
- For example, can be written as .
Collecting Like Terms
- Like terms have the same variables with the same powers.
- For example, a and are not like terms and cannot be combined.
- To collect like terms, add or subtract the coefficients, for example .
Simplifying an Expression Step by Step
- First expand brackets using the distributive law.
- Then use exponents and collect like terms to simplify fully.
Practice Questions
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Simplify the expression: .
Correct! 🎉 +10 pointsNot quite right
To simplify , we apply exponents. Since x occurs 3 times in the multiplication, the expression becomes .
Simplify .
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When simplifying , we combine like terms by adding their coefficients. , so the simplified expression is .
Are and like terms?
Correct! 🎉 +20 pointsNot quite right
and are not like terms because they have different exponents. has an exponent of 1 for a, whereas has an exponent of 2.
Simplify .
Correct! 🎉 +20 pointsNot quite right
To simplify , collect like terms. Combine and to get . Combine and to get . Thus, the simplified expression is .
Are and like terms?
Correct! 🎉 +20 pointsNot quite right
and are not like terms because they have different variables and exponents. has , whereas has .
Simplify .
Correct! 🎉 +30 pointsNot quite right
First, combine like terms. . Next, note that is the same as , so . Thus, the simplified expression is .
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Simplifying Expressions with Multiple Variables
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Students Also Ask
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Two terms are like terms when they have exactly the same variables raised to exactly the same exponents. For example, 2a²b and 5a²b are like terms, because both use a² and b. Only the coefficient in front may be different, and the order of the letters does not matter.
The terms a and a² use the same letter, but their exponents are different. The term a has an exponent of 1, while a² has an exponent of 2. Like terms must share the same exponents, so a and a² cannot be collected into a single term.
A coefficient is the number written in front of the variables in a term. In 5ab the coefficient is 5, and in ab the coefficient is 1. When you collect like terms, you add the coefficients together while keeping the variables exactly the same.
Yes. Expand any brackets first, using the distributive law, so every term is written out in full. Next, apply exponents wherever a variable repeats. Finally, collect the like terms. Expanding first makes sure you do not miss like terms that were hidden inside the brackets.
Multiplication is commutative, which means the order of the factors does not change the result. So y × x × y simplifies to the same term as x × y × y, which is xy². You can rearrange the factors freely before you write them with exponents.