Factorising Expressions Worksheet

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Part 1: Learn the process

WALT: We Are Learning To factorise simple algebraic expressions, write products using brackets, and check by expanding.

Success criteria: I can find the greatest common factor (GCF). I can write the expression as a product. I can expand to check that both forms are equivalent.

Worked example

🟦 6x + 12

The greatest common factor is 🟦 6.

Divide each term by 6: 6x ÷ 6 = x and 12 ÷ 6 = 2.

So, 6x + 12 = 6(x + 2).

Check by expanding: 6(x + 2) = 6x + 12 ✓

Four steps

1. Find the greatest common factor.

2. Divide each term by the common factor.

3. Write the remaining terms inside brackets.

4. Expand to check your answer.

1. Complete the scaffold: 8p + 24 = 8(__________). Check: 8(__________) = __________.

Optional oral response: Tell a partner: “The common factor is ______ because ______.”

Dyslexia-friendly option: Read the four steps aloud, use the colour symbols, or explain your answer orally to a partner or teacher.

Part 2: Record, factorise and check

For each expression, find the GCF, write the factorised form, and expand it to check.

Recording table

Expression: 3x + 9 GCF: ______ Factorised form: ____________________ Expansion check: ____________________

Expression: 4a + 20 GCF: ______ Factorised form: ____________________ Expansion check: ____________________

Expression: 5x + 15 GCF: ______ Factorised form: ____________________ Expansion check: ____________________

Expression: 4y + 28 GCF: ______ Factorised form: ____________________ Expansion check: ____________________

Expression: 7n + 21 GCF: ______ Factorised form: ____________________ Expansion check: ____________________

Expression: 9r + 18 GCF: ______ Factorised form: ____________________ Expansion check: ____________________

2. Show your working for any two expressions above.

Partner check: Explain one answer. Your partner can respond, “I agree because…” or “I checked by…”.

Part 3: Apply and exit ticket

3. A fictional kapa haka resource plan has 6 organised groups, with each group needing q + 3 resources. Explain what the factors in 6(q + 3) could represent.

Extension: Factorise −3x − 12 and explain why x + 5 cannot be factorised further using a common factor greater than 1.

Exit ticket

4a. Factorise: 6q + 18 = ____________________

4b. Expand your answer to check: ________________________________

4c. In one sentence, explain what the factors could represent in a fictional resource plan.

Support: You may use the sentence frame: “The outside factor represents __________ groups, and the bracket represents __________ resources in each group.” You may write, draw a quick model, or give an oral response.