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Maths · Algebra Foundations

Simplify expressions

Combine like terms and expand simple brackets.

Not startedCAMBRIDGE · 7CBSE · VIIIB · MYP-1

What Are Like Terms?

Like terms are parts of an expression that have exactly the same letter part. For example, 3x and 5x are like terms. We can add or subtract like terms by combining their numbers. Think of x as a type of fruit: 3 apples plus 5 apples equals 8 apples!

Combining Like Terms

To simplify an expression, collect all the like terms together. Add or subtract the numbers in front (called coefficients). The letter part stays the same. For example: 4a + 2a = 6a. Remember, 3x and 3y are not like terms because the letters differ.

Expanding Brackets

When you see a number outside brackets, multiply it by everything inside. This is called expanding or distributing. For example: 3(x + 2) means 3 times x, plus 3 times 2, which gives 3x + 6. Each term inside gets multiplied.

Expanding Then Simplifying

Sometimes you need to expand brackets first, then collect like terms. For example: 2(x + 3) + 4x becomes 2x + 6 + 4x, which simplifies to 6x + 6. Always expand first, then tidy up by combining like terms.

Watch Out for Negatives

Be careful with minus signs! When expanding −2(x + 3), multiply both terms by −2 to get −2x − 6. When combining like terms such as 5x − 2x, subtract the coefficients to get 3x. Negatives follow the usual addition and subtraction rules.

Worked examples

  1. 1. Simplify 7y + 3y − 2y

    1. All three terms have the same letter y, so they are like terms.
    2. Combine the coefficients: 7 + 3 − 2 = 8.
    3. The answer is 8y.

  2. 2. Expand and simplify 4(a + 2) + 3a

    1. Expand the bracket: 4 × a = 4a and 4 × 2 = 8, giving 4a + 8.
    2. Now the expression is 4a + 8 + 3a.
    3. Combine like terms: 4a + 3a = 7a.
    4. The answer is 7a + 8.

  3. 3. Simplify 5x + 2y − 3x + y

    1. Identify like terms: 5x and −3x are like terms; 2y and y are like terms.
    2. Combine x terms: 5x − 3x = 2x.
    3. Combine y terms: 2y + y = 3y.
    4. The answer is 2x + 3y.

Try it yourself

Simplify 6m + 4m − 3m

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