Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Expand and simplify 6(w + 2) − 2(w + 5).
Show worked solution
6w + 12 − 2w − 10 = 4w + 2. 4w + 17 only multiplies the first term of the second bracket (−2w + 5); 4w + 22 is the sign error −2 × 5 = +10; 8w + 2 is the sign error −2 × w = +2w.
2 Expand and simplify 2x(x + 5) − 3x.
Show worked solution
2x(x + 5) = 2x2 + 10x, and 10x − 3x = 7x. So the answer is 2x2 + 7x.
3 Expand and simplify 4(3c − 2) − 5c, then find its value when c = 4.
Show worked solution
12c − 8 − 5c = 7c − 8. With c = 4: 28 − 8 = 20. Check in the original: 4(12 − 2) − 20 = 40 − 20 = 20 ✓.
Level 2 · Core
4 Expand and simplify −4b(2b − 3) + 3(b2 − 4b).
Show worked solution
−8b2 + 12b + 3b2 − 12b. The b terms cancel, leaving −5b2. −5b2 − 24b is the sign error −4b × −3 = −12b; −5b2 + 8b only multiplies the first term of the second bracket (3b2 − 4b); −5b2 + 24b is the sign error 3 × −4b = +12b.
5 Expand and simplify 3m2(2m − 1) − m(4m2 − 7m).
Show worked solution
3m2(2m − 1) = 6m3 − 3m2 and −m(4m2 − 7m) = −4m3 + 7m2. Collect: 6m3 − 4m3 = 2m3 and −3m2 + 7m2 = 4m2. Answer: 2m3 + 4m2.
6 Expand and simplify 5(2q − 3) − 2(3q − 8), then find its value when q = −4.
Show worked solution
10q − 15 − 6q + 16 = 4q + 1. With q = −4: 4(−4) + 1 = −15. Check in the original: 5(−11) − 2(−20) = −55 + 40 = −15 ✓.
Level 3 · Challenge
7 Three statements:
1 x(x − 4) − (x2 − 4x) = 0
2 −3t(2 − t) = −6t − 3t2
3 2(5 − k) − 3(k − 5) = 25 − 5k
Which statements are correct?
1 x(x − 4) − (x2 − 4x) = 0
2 −3t(2 − t) = −6t − 3t2
3 2(5 − k) − 3(k − 5) = 25 − 5k
Which statements are correct?
Show worked solution
x2 − 4x − x2 + 4x = 0 (1 ✓). −3t × −t = +3t2, so −3t(2 − t) = −6t + 3t2, not −6t − 3t2 (2 ✗). 10 − 2k − 3k + 15 = 25 − 5k (3 ✓). 1 and 3.
8 2x(ax − 5) − 3(bx − 4) = 8x2 − 16x + 12 for every value of x. Find the numbers a and b.
Show worked solution
The left side is 2ax2 − 10x − 3bx + 12. Matching x2: 2a = 8, so a = 4. Matching x: −10 − 3b = −16, so 3b = 6 and b = 2. The constant 12 matches as a check.
9 A rectangle 4x by (3x + 2) has a smaller rectangle 3 by (x − 1) cut out of it. Write the area left as one expanded expression, then find its value when x = 5.
Show worked solution
4x(3x + 2) − 3(x − 1) = 12x2 + 8x − 3x + 3 = 12x2 + 5x + 3. With x = 5: 300 + 25 + 3 = 328. Check: 20 × 17 − 3 × 4 = 340 − 12 = 328 ✓.