Mind the Mistake, Mend the Mistake — We Distribute Yet Things Multiply

1. 16 marksGanita Prakash Cl-8 Part 1, §6.3, page 150

   For each of the twelve simplifications below, check whether there is a mistake; if so explain what went wrong and write the correct expression. (1) −3p(−5p + 2q) = −3p + 5p − 2q = p − 2q. (2) 2(x − 1) + 3(x + 4) = 2x − 1 + 3x + 4 = 5x + 3. (3) y + 2(y + 2) = (y + 2)² = y² + 4y + 4. (4) (5m + 6n)² = 25m² + 36n². (5) (−q + 2)² = q² − 4q + 4. (6) 3a(2b × 3c) = 6ab × 9ac = 54a²bc. (7) ½(10s − 6) + 3 = 5s − 3 + 3 = 5s. (8) 5w² + 6w = 11w². (9) 2a³ + 3a³ + 6a²b + 6ab² = 5a³ + 12a²b². (10) (a + 2)(b + 4) = ab + 8. (11) ab² + a²b + a²b² = ab(a + b + ab). (12) (x + 2)(x + 5) = (x + 2)x + (x + 2)5 = x² + 2x + 5x + 10 = x² + 7x + 10.

   Hint. Not every one is wrong — four of the twelve are already correct. Check each by expanding independently.

   Note on sources: the book's printed answer key does not cover this section, so each item below has been worked out from first principles and independently re-expanded.

   Eight contain mistakes; four (numbers 5, 7, 11 and 12) are already correct.

   (1) ✗ Wrong. The −3p was added instead of multiplied. Distribution means multiplying the outside term by each term inside: −3p(−5p + 2q) = (−3p)(−5p) + (−3p)(2q) = 15p² − 6pq

   (2) ✗ Wrong. The multipliers were applied only to the first term in each bracket. 2 × (−1) = −2, not −1; and 3 × 4 = 12, not 4. 2(x − 1) + 3(x + 4) = 2x − 2 + 3x + 12 = 5x + 10

   (3) ✗ Wrong. The leading y was wrongly absorbed into a factor, turning a sum into a square. y + 2(y + 2) = y + 2y + 4 = 3y + 4

   (4) ✗ Wrong. The middle term of the square is missing — squaring a sum is not squaring each part. (5m + 6n)² = (5m)² + 2(5m)(6n) + (6n)² = 25m² + 60mn + 36n²

   (5) ✓ Correct. (−q + 2)² = (−q)² + 2(−q)(2) + 2² = q² − 4q + 4 ✓

   (6) ✗ Wrong. Distribution applies over addition, not over multiplication — the 3a was wrongly spread across both factors, using it twice. 3a(2b × 3c) = 3a × 6bc = 18abc

   (7) ✓ Correct. ½(10s − 6) + 3 = 5s − 3 + 3 = 5s ✓

   (8) ✗ Wrong. w² and w are unlike terms and cannot be added. 5w² + 6w is already in its simplest form: 5w² + 6w

   (9) ✗ Wrong. 2a³ + 3a³ = 5a³ is fine, but 6a²b and 6ab² are unlike — the letters carry different powers — so they cannot be merged into 12a²b². 5a³ + 6a²b + 6ab²

   (10) ✗ Wrong. Only the first terms and the last terms were multiplied; the two cross terms were dropped. (a + 2)(b + 4) = ab + 4a + 2b + 8

   (11) ✓ Correct. ab(a + b + ab) = a²b + ab² + a²b² ✓ — the same three terms.

   (12) ✓ Correct. Every step is sound and the final answer checks out ✓

   The four error types to learn from this set:

   1. Adding instead of multiplying when distributing — items 1 and 3.
   2. Distributing to only some terms — items 2 and 10.
   3. Forgetting the middle term of a square — item 4.
   4. Combining unlike terms — items 8 and 9. Plus one structural error: distributing over a product instead of a sum — item 6.

   ✦ Correct as printed: 5, 7, 11, 12. Corrections: (1) 15p² − 6pq, (2) 5x + 10, (3) 3y + 4, (4) 25m² + 60mn + 36n², (6) 18abc, (8) 5w² + 6w, (9) 5a³ + 6a²b + 6ab², (10) ab + 4a + 2b + 8.

Solutions written by the tuition.in editorial team and checked against the NCERT Class 8 Mathematics textbook Ganita Prakash Part 1, Reprint 2026-27 (hegp106.pdf). The chapter develops the distributive property into the three standard identities — 1A (a+b)², 1B (a−b)², 1C (a+b)(a−b) — via a multiplication-grid model, then applies them to fast mental multiplication and to area/tile patterns. Every expansion here was independently re-expanded term by term and every numeric answer recomputed before comparison with the book's printed answer key. TWO NOTES: (1) the twelve 'Mind the Mistake, Mend the Mistake' items on page 150 have NO answers in the printed key — each has been worked out from first principles here, including identifying which four of the twelve are in fact already correct, and this is stated openly in the solution; (2) the circle-pattern activity in §6.4 ('This Way or That Way') is omitted because the circle counts cannot be recovered from the text without the printed figure.. Questions are referenced from the NCERT textbook for identification.