Lesson title: Collecting like terms

Do now (revision)

If \(x = 3\), find the value of:

  1. \(2x\)

  2. \(x + 5\)

  1. \(4x - 2\)

  2. \(\dfrac{x}{3}\)

Finished early? Try: If \(a = 4\) and \(b = 2\), find \(3a + b\)

Algebra: collecting like terms

By the end of this lesson, you will be able to:

  • Identify like terms in an expression
  • Collect like terms to simplify expressions
  • Check your answers by substitution

Copy these.

‘Like terms’:

  • \(3x\) and \(7x\) ✓
  • \(2ab\) and \(5ab\) ✓
  • \(4\) and \(9\) ✓

Not ‘like terms’:

  • \(3x\) and \(3y\) ✗
  • \(2a\) and \(2a^2\) ✗

Answer this: Look at the examples you just copied. What do the terms in each group have in common? Write down what you notice.

Are they like terms?

\(5p\) and \(2p\)

\(3m\) and \(3n\)

\(7\) and \(12\)

\(4xy\) and \(9xy\)

\(2a\) and \(2b\)

\(6k\) and \(k\)

Collecting Like Terms

Copy this example:

To simplify \(3a + 5a\):

  1. Check they’re like terms (✓ both have ‘a’)
  2. Add the numbers: \(3 + 5 = 8\)
  3. Keep the letter: \(8a\)

So: \(3a + 5a = 8a\)

Worked example 1

Try to guess the next step:

To simplify: \(4m + 2m + m\)

  1. Check they’re like terms ✓
  2. Add the coefficients: \(4+2+1 = 7\)
  3. Keep the letter: \(7m\)

So \(4m + 2m + m = 7m\)

How would you check your answers?

Worked Example 2

Try to guess the next step:

To simplify \(8k - 3k\):

  1. Check they’re like terms ✓
  2. Subtract the coefficients: \(8 - 3 = 5\)
  3. Keep the letter: \(5k\)
  4. So: \(8k - 3k = 5k\)

Your turn: Simplify these expressions (if possible):

  1. \(2x + 6x\)

  2. \(5p - 3p\)

  3. \(n + 4p\)

  4. \(10p - 7p\)

  1. \(7a + a\)

  2. \(3b - 2b + 4b\)

  3. \(m + 2m + p\)

  4. \(7a - 4a - a\)

Mixed Terms: Example 1

Watch and listen

Simplify: \(3a + 2b + 5a\)

Mixed terms: example 2

Guess the next step:

Simplify: \(4x + 3y + 2x - y\)

Solution:

Your Turn 3

Simplify these expressions:

  1. \(2a + 3b + 4a\)
  2. \(5m + 2n + 3m\)
  3. \(6x + 4y - 2x\)
  4. \(7p + 3q - 2p + q\)

Remember: Only collect like terms!

Your turn: simplify the following:

  1. \(4a + 6 + 2a\)

  2. \(3m + 7 + m + 2\)

  1. \(5x + 4 - 2x + 1\)

  2. \(6p + 3 - p - 1\)

Common Mistakes

Just listen

Watch out for these:

❌ \(3x + 2y = 5xy\) Wrong! (not like terms)

❌ \(4a + 3 = 7a\) Wrong! (different types)

❌ \(2m + 2n = 4mn\) Wrong! (not like terms)

✓ \(3x + 2y\) stays as \(3x + 2y\)

✓ \(4a + 3\) stays as \(4a + 3\)

✓ \(2m + 2n\) stays as \(2m + 2n\)

Checking Your Work by substitution

Example: Did I simplify \(3x + 5x\) correctly to get \(8x\)?

Check: Let \(x = 2\)

  • Original: \(3(2) + 5(2) = 6 + 10 = 16\)
  • Answer: \(8(2) = 16\) ✓

If they match, you’re correct!

Complete these, showing all working:

  1. \(7a + 2a - 3a\)
  2. \(4m + 3n + 2m + n\)
  3. \(5x + 8 - 2x + 3\)
  4. \(6p + 4q - p - 2q\)
  5. \(3a + 2b + a - b + 5\)

For Q5, check your answer using \(a = 2\) and \(b = 3\)

Early finishers: Complete Ex 3.05

Summary

What we learned:

  • Like terms have the same variables
  • We can add or subtract like terms
  • Different letters stay separate
  • Always check by substitution

Key skill: Look for matching letters!

Exit Ticket

On a piece of paper, complete:

  1. Are \(4m\) and \(7m\) like terms? (Yes/No)
  2. Simplify: \(5x + 3x\)
  3. Simplify: \(2a + 4b + 3a\)

Hand in as you leave