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NCERT Solutions Ganita Prakash (Part 1) Chapter 4 –95Section 4.4 Simplification of Algebraic Expressions — Mind the Mistake, Mend the Mistake

Book page 94 Updated on2026-09-05

Q1.
3a + 2b → Simplest Form given: 5
Answer

Mistake. Unlike terms were added.

Correct simplest form: 3a + 2b
Why it happens: 3 and 2 were added while the letters were thrown away. But a and b are different letter-numbers, so 3a and 2b are unlike terms and cannot be merged.
Q2.
3b – 2b – b → Simplest Form given: 0
Answer

No mistake.

3b – 2b – b = (3 – 2 – 1)b = 0 × b = 0
Q3.
6 (p + 2) → Simplest Form given: 6p + 8
Answer

Mistake. The 6 was multiplied only by p, and then added to 2.

6 (p + 2) = 6 × p + 6 × 2
= 6p + 12
Why it happens: The distributive property says the multiplier reaches every term inside the bracket.
Q4.
(4x + 3y) – (3x + 4y) → Simplest Form given: x + y
Answer

Mistake. The sign of the y-term was not changed.

(4x + 3y) – (3x + 4y)
= 4x + 3y – 3x – 4y
= (4 – 3)x + (3 – 4)y
= x – y
Q5.
5 – (2 – 6z) → Simplest Form given: 3 – 6z
Answer

Mistake. Only the first term inside the bracket had its sign changed.

5 – (2 – 6z) = 5 – 2 + 6z
= 3 + 6z
Check it yourself: For z = 1, 5 – (2 – 6) = 5 – (–4) = 9, and 3 + 6 = 9 ✔, while 3 – 6 = –3 ✘.
Q6.
2 + (x + 3) → Simplest Form given: 2x – 6
Answer

Mistake. The bracket was treated as a multiplication.

2 + (x + 3) = 2 + x + 3
= x + 5
Why it happens: There is a plus sign before the bracket, so the bracket can simply be dropped.
Q7.
2y + (3y – 6) → Simplest Form given: – y + 6
Answer

Mistake. The signs inside were flipped even though the bracket has a plus in front.

2y + (3y – 6) = 2y + 3y – 6
= 5y – 6
Q8.
7p – p + 5q – 2q → Simplest Form given: 7p + 3q
Answer

Mistake. The – p was left out.

7p – p + 5q – 2q
= (7 – 1)p + (5 – 2)q
= 6p + 3q
Tip: A letter written alone, like p, means 1p. It must be counted.
Q9.
5 (2w + 3x + 4w) → Simplest Form given: 10w + 15x + 20w
Answer

Mistake. The distribution was done correctly, but like terms were not collected — so it is not the simplest form.

5 (2w + 3x + 4w) = 5 (6w + 3x)
= 30w + 15x
Tip: Add like terms inside the bracket first — 2w + 4w = 6w — and the work becomes shorter.
Q10.
3j + 6k + 9h + 12 → Simplest Form given: 3 (j + 2k + 3h + 4)
Answer

Mistake. The answer is correct as an equal expression, but it is not in simplest form because the bracket is still there.

Correct simplest form: 3j + 6k + 9h + 12
Why it happens: In this chapter ‘simplest form’ means brackets removed, like terms added and number terms added. The given expression is already like that — nothing needed to change.
Q11.
4 (2r + 3s + 5) → Simplest Form given: – 20 – 8r – 12s
Answer

Mistake. Every term was given a minus sign, though there is no minus anywhere.

4 (2r + 3s + 5) = 4 × 2r + 4 × 3s + 4 × 5
= 8r + 12s + 20
Q12.
Take a look at all the corrected simplest forms (i.e. brackets are removed, like terms are added, and terms with only numbers are also added). Is there any relation between the number of terms and the number of letter-numbers these expressions have?
Answer
No.Correct simplest formNumber of termsNumber of letter-numbers
13a + 2b22
2010
36p + 1221
4x – y22
53 + 6z21
6x + 521
75y – 621
86p + 3q22
930w + 15x22
103j + 6k + 9h + 1243
118r + 12s + 2032

Yes. In every row, the number of letter-numbers is never more than the number of terms:

Number of letter-numbers ≤ Number of terms
Why it happens: Once an expression is fully simplified, each letter-number can appear in only one term — all its like terms have already been merged. There may also be one extra term made of numbers alone, which carries no letter. So terms can be more than letters, but never fewer.
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