Simplifying Expressions

Q: What does it mean to simplify an expression?

Simplifying an expression means rewriting it in its shortest equal form. You expand any brackets, then collect like terms by adding their coefficients, until no like terms remain. The result has fewer terms but exactly the same value, making it quicker to read and use.

Q: How do you know if two terms are like terms?

Two terms are like terms when they contain exactly the same variable raised to the same power. For example, 6x and -4x are like terms because both contain x. However, x and x² are not, because their powers differ. Only like terms can be collected.

Q: What is the distributive law?

The distributive law tells you to multiply each term inside a set of brackets by the term outside. For example, 2(3 + x) becomes 6 + 2x. It lets you remove brackets while keeping the expression's value the same, which is the start of expanding brackets.

Q: What happens when there is a minus sign in front of the brackets?

A minus sign in front of brackets works like multiplying by -1. So you reverse the sign of every term inside. For example, -(x - 3) becomes -x + 3. Changing all the signs keeps the expression equal to the original before you collect like terms.

Q: Why do you collect like terms?

You collect like terms to make an expression shorter without changing its value. Adding the coefficients of terms with the same variable turns 6x - 4x into 2x. Fewer terms make the expression easier to read, substitute into, and solve. That is why it is the final step.

Key concept

Simplifying expressions means rewriting them in their shortest equal form. First expand brackets, like 2(3 + x) = 6 + 2x, then collect like terms. Only terms with the same letter and power can be collected.

Simplifying Expressions - introduction visual

Video Lesson

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Flashcards

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Steps to simplify an expression by expanding brackets and collecting like terms, showing -5x + 2(3 + x) simplified to -3x + 6.

Simplifying expressions by expanding brackets using distributive law, and collecting like terms to simplify 3(2x - 1) + 4(-x + 5) into 2x + 17.

How to Simplify an Expression?

Expand brackets first using the distributive law.
Then collect like terms by adding or subtracting their coefficients.

Practice Questions

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Q1Easy

Simplify the expression: $5 y + 3 y - 2 y$ .

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Interactive Activity

Simplifying Expressions: Expand brackets and collect terms

Click to Expand

++-

Click to Combine Like Terms

Simplified!

Step 1: Expand

Start by expanding the brackets. Multiply 2 into the first group: 6x + 8. Then multiply 5 into the second group: 5x - 10.

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Students Also Ask

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What does it mean to simplify an expression?

Simplifying an expression means rewriting it in its shortest equal form. You expand any brackets, then collect like terms by adding their coefficients, until no like terms remain. The result has fewer terms but exactly the same value, making it quicker to read and use.

How do you know if two terms are like terms?

Two terms are like terms when they contain exactly the same variable raised to the same power. For example, 6x and -4x are like terms because both contain x. However, x and x² are not, because their powers differ. Only like terms can be collected.

What is the distributive law?

The distributive law tells you to multiply each term inside a set of brackets by the term outside. For example, 2(3 + x) becomes 6 + 2x. It lets you remove brackets while keeping the expression's value the same, which is the start of expanding brackets.

What happens when there is a minus sign in front of the brackets?

A minus sign in front of brackets works like multiplying by -1. So you reverse the sign of every term inside. For example, -(x - 3) becomes -x + 3. Changing all the signs keeps the expression equal to the original before you collect like terms.

Why do you collect like terms?

You collect like terms to make an expression shorter without changing its value. Adding the coefficients of terms with the same variable turns 6x - 4x into 2x. Fewer terms make the expression easier to read, substitute into, and solve. That is why it is the final step.

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