Mathematics • Year 7 • Unit 2 • Lesson 4

Collecting Like Terms

Build the basics: tell like and unlike terms apart, group like terms, combine coefficients (keeping the variable), and simplify expressions step by step, including signs and constants.

Build · I Do / We Do / You Do

1. I do, fully worked example

Read every line. Each step has a short reason on the right so you can see why, not just what.

Problem. Simplify 4a + 3b − 7a + 2 − 2b + 5.

Step 1, List every term with its sign.

4a, +3b, −7a, +2, −2b, +5

Reason: terms are separated by + and −. The sign belongs to the term that follows.

Step 2, Group like terms (a's, b's, constants).

(4a − 7a) + (3b − 2b) + (2 + 5)

Reason: like terms have the SAME variable. a-terms group together; b-terms group together; numbers (constants) group together.

Step 3, Combine each group (add coefficients only, variable stays).

4a − 7a = (4 − 7)a = −3a

3b − 2b = (3 − 2)b = b

2 + 5 = 7

Reason: only coefficients are added or subtracted. The variable part is unchanged. 1b is just written as b.

Step 4, Write the simplified expression.

−3a + b + 7

Answer: −3a + b + 7 (or equivalently b − 3a + 7).

Stuck? Revisit lesson § "The Full Process", sort, group, combine, finish. The variable never disappears.

2. We do, fill in the missing steps

Fill in each blank line. 4 marks

Problem. Simplify 6x + 5 − 2x + 3y − 4 − y.

Step 1, List every term with its sign:

6x, ______, ______, ______, ______, ______

Step 2, Group like terms:

(______ + ______) + (______ + ______) + (______ + ______)

Step 3, Combine each group:

x-terms: ______ y-terms: ______ constants: ______

Step 4, Final answer:

______________________

Stuck? Watch the signs: −y means −1y. The constants are +5 and −4.

3. You do, independent practice

Show working under each. The first four are foundation, the middle two are standard, and the last two are extension.

Foundation, single step

3.1 Simplify 3x + 5x. 1 mark

3.2 Simplify 8a − 3a. 1 mark

3.3 Are 4n and 4m like terms? Why or why not? 1 mark

3.4 Simplify 4y − 7y. (Watch the sign of your answer.) 1 mark

Standard, combine two ideas

3.5 Simplify 2x + 7 + 5x − 3. 2 marks

3.6 Simplify 4a + 3b + 2a − b. 2 marks

Extension, push your thinking

3.7 Simplify 5m + 2n − 8m − 5n + 3m + 6. 3 marks

3.8 Simplify 3x + 4 − x + 5y + 2x − 5y − 4. What happens to the y terms? What happens to the constants? 2 marks

Stuck on 3.8? Sometimes coefficients cancel completely. If 5y − 5y = 0, the y disappears. Same idea for constants.

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Answers, Do not peek before attempting

Section 2, We do (6x + 5 − 2x + 3y − 4 − y)

Step 1: 6x, +5, −2x, +3y, −4, −y.
Step 2: (6x − 2x) + (3y − y) + (5 − 4).
Step 3: x-terms = 4x; y-terms = 2y; constants = 1.
Step 4: 4x + 2y + 1.

3.1-3x + 5x

= (3 + 5)x = 8x. (Add coefficients only, variable stays.)

3.2-8a − 3a

= (8 − 3)a = 5a.

3.3, Are 4n and 4m like terms?

No. Like terms must have the SAME variable. The coefficients match (both 4), but n ≠ m, so they are unlike terms and cannot be combined.

3.4-4y − 7y

= (4 − 7)y = −3y. (Yes, a negative coefficient is fine. The variable y stays.)

3.5-2x + 7 + 5x − 3

x-terms: 2x + 5x = 7x. Constants: 7 − 3 = 4. Answer: 7x + 4.

3.6-4a + 3b + 2a − b

a-terms: 4a + 2a = 6a. b-terms: 3b − b = 2b. Answer: 6a + 2b.

3.7-5m + 2n − 8m − 5n + 3m + 6

m-terms: 5m − 8m + 3m = (5 − 8 + 3)m = 0m = 0. n-terms: 2n − 5n = −3n. Constant: 6. Answer: −3n + 6 (or 6 − 3n).

3.8-3x + 4 − x + 5y + 2x − 5y − 4

x-terms: 3x − x + 2x = 4x. y-terms: 5y − 5y = 0 (cancel, disappear). Constants: 4 − 4 = 0 (cancel, disappear). Answer: 4x. The y terms and the constants cancelled completely.