Expanding & Factorising — Year 8 Practice Questions
Work through these Year 8 practice questions on expanding and factorising. Try each one before revealing the worked solution.
Questions
Expand 5(x + 2).
Expand 3(2x − 4).
Expand −2(x + 5).
Expand and simplify 4(x + 3) + 2x.
Factorise 6x + 8.
Factorise 10x − 15.
Factorise fully 12x + 18.
Factorise x² + 5x.
Answers & Worked Solutions
Question 1 Solution
Step 1: Multiply both terms by 5.
Step 2: 5 × x = 5x and 5 × 2 = 10, giving 5x + 10.
Answer: 5x + 10
Question 2 Solution
Step 1: 3 × 2x = 6x and 3 × (−4) = −12.
Step 2: So 3(2x − 4) = 6x − 12.
Answer: 6x − 12
Question 3 Solution
Step 1: −2 × x = −2x and −2 × 5 = −10.
Step 2: So −2(x + 5) = −2x − 10.
Answer: −2x − 10
Question 4 Solution
Step 1: Expand: 4x + 12 + 2x.
Step 2: Collect like terms: 6x + 12.
Answer: 6x + 12
Question 5 Solution
Step 1: The highest common factor of 6 and 8 is 2.
Step 2: 6x + 8 = 2(3x + 4).
Answer: 2(3x + 4)
Question 6 Solution
Step 1: The highest common factor of 10 and 15 is 5.
Step 2: 10x − 15 = 5(2x − 3).
Answer: 5(2x − 3)
Question 7 Solution
Step 1: The highest common factor of 12 and 18 is 6.
Step 2: 12x + 18 = 6(2x + 3).
Answer: 6(2x + 3)
Question 8 Solution
Step 1: Both terms share a factor of x.
Step 2: x² + 5x = x(x + 5).
Answer: x(x + 5)
Build strong foundations in Expanding & Factorising
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