We Distribute, Yet Things Multiply — Class 8 MCQs with Answers
Class 8 CBSE Mathematics · Chapter 6
72 practice questions · 24 Easy · 24 Medium · 24 Hard · Updated
Practise the most important Class 8 CBSE Mathematics questions from Chapter 6, "We Distribute, Yet Things Multiply". You get 9 timed quizzes made from 72 NCERT-based MCQs, with answers and explanations. The questions are split into 24 Easy, 24 Medium and 24 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams get right.
To score well in "We Distribute, Yet Things Multiply", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on We Distribute, Yet Things Multiply, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 8 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
We Distribute, Yet Things Multiply — important questions & MCQs with answers (Class 8 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation.
- Q1Easy
The distributive property states that a × (b + c) equals:
A.a×b + a×c✓ CorrectB.a×b × a×cC.a + b × cD.ab + cAnswer: A. a×b + a×c
Explanation: The distributive property multiplies a into each term inside the bracket: a × (b + c) = a×b + a×c. The two products are added, not multiplied together.
- Q2Easy
The identity for (a + b)² is:
A.a² + b²B.a² + 2ab + b²✓ CorrectC.a² − 2ab + b²D.2a + 2bAnswer: B. a² + 2ab + b²
Explanation: Squaring a sum uses the identity (a + b)² = a² + 2ab + b² — the middle term 2ab is essential. Dropping it gives the common mistake a² + b².
- Q3Easy
Is (a + b)² equal to a² + b²?
A.Yes, alwaysB.Only when a = bC.No, it also has the middle term 2ab✓ CorrectD.Only when b = 1Answer: C. No, it also has the middle term 2ab
Explanation: (a + b)² = a² + 2ab + b², so it equals a² + b² only when the middle term 2ab is zero — not as a general rule. The middle term is always present unless a or b is 0.
- Q4Easy
Using (a + b)², find 21² = (20 + 1)².
A.401B.420C.441✓ CorrectD.431Answer: C. 441
Explanation: 21² = (20 + 1)² = 20² + 2×20×1 + 1² = 400 + 40 + 1 = 441. Forgetting the middle term 2×20×1 = 40 gives the wrong 401.
- Q5Easy
Using distribution, 6 × 13 = 6×10 + 6×3 equals:
A.68B.63C.180D.78✓ CorrectAnswer: D. 78
Explanation: Distribute the 6 to both parts: 6×10 = 60 and 6×3 = 18, then add: 60 + 18 = 78. Multiplying the two products together instead of adding gives the wrong total 180.
- Q6Easy
The identity for (a − b)² is:
A.a² + b²B.a² + 2ab + b²C.a² − 2ab + b²✓ CorrectD.a² − b²Answer: C. a² − 2ab + b²
Explanation: Squaring a difference gives (a − b)² = a² − 2ab + b², with a plus sign before b². Writing a² − b² skips the middle term entirely.
- Q7Medium
Expand (x + 2)(x + 5).
A.x² + 7x + 10✓ CorrectB.x² + 10x + 7C.x² + 7x + 7D.x² + 10Answer: A. x² + 7x + 10
Explanation: (x + 2)(x + 5) = x² + (2 + 5)x + 2×5 = x² + 7x + 10 — the middle coefficient is the sum 2 + 5, the constant is the product 2×5. Swapping these roles gives the wrong x² + 10x + 7.
- Q8Medium
Expand (x + 3)².
A.x² + 6x + 9✓ CorrectB.x² + 9C.x² + 3x + 9D.x² + 6x + 6Answer: A. x² + 6x + 9
Explanation: (x + 3)² = x² + 2×x×3 + 3² = x² + 6x + 9. Using the constant alone for the middle term instead of 2×x×3 gives the wrong x² + 3x + 9.
- Q9Medium
Rahul writes (a + b)² = a² + b². What has he left out?
A.the term b²B.the middle term 2ab✓ CorrectC.the term a²D.nothing, it is correctAnswer: B. the middle term 2ab
Explanation: The correct expansion is (a + b)² = a² + 2ab + b², so a² + b² is missing the middle term 2ab. Squaring a sum is not the same as squaring each term separately.
- Q10Medium
Using an identity, evaluate 104².
A.10816✓ CorrectB.10616C.10800D.11016Answer: A. 10816
Explanation: 104² = (100 + 4)² = 10000 + 2×100×4 + 16 = 10000 + 800 + 16 = 10816. Forgetting to add the final +16 gives the wrong 10800.
- Q11Medium
Expand (x + 6)(x − 2).
A.x² − 4x − 12B.x² + 4x + 12C.x² + 8x − 12D.x² + 4x − 12✓ CorrectAnswer: D. x² + 4x − 12
Explanation: (x + 6)(x − 2) = x² + (6 − 2)x + 6×(−2) = x² + 4x − 12. Adding the outer numbers as 6 + 2 = 8 instead of 6 − 2 = 4 gives the wrong x² + 8x − 12.
- Q12Hard
Expand (2x + 3y)².
A.4x² + 9y²B.4x² + 12xy + 9y²✓ CorrectC.4x² + 6xy + 9y²D.2x² + 12xy + 9y²Answer: B. 4x² + 12xy + 9y²
Explanation: (2x + 3y)² = (2x)² + 2×2x×3y + (3y)² = 4x² + 12xy + 9y². Using half the cross term (6xy) instead of the full 12xy gives the wrong 4x² + 6xy + 9y².
- Q13Hard
Evaluate 1002² using an identity.
A.1004004✓ CorrectB.1002004C.1000404D.1004040Answer: A. 1004004
Explanation: 1002² = (1000 + 2)² = 1000000 + 2×1000×2 + 4 = 1000000 + 4000 + 4 = 1004004. Using half the middle term (2000) instead of the full 4000 gives the wrong 1002004.
- Q14Hard
Expand (5a − 4b)².
A.25a² + 16b²B.25a² − 40ab + 16b²✓ CorrectC.25a² − 20ab + 16b²D.25a² − 40ab − 16b²Answer: B. 25a² − 40ab + 16b²
Explanation: (5a − 4b)² = (5a)² − 2×5a×4b + (4b)² = 25a² − 40ab + 16b². Using half the cross term (10ab) instead of the full 40ab gives the wrong 25a² − 20ab + 16b².
Key concepts: We Distribute, Yet Things Multiply (Class 8 Mathematics)
This chapter turns the distributive property into a powerful tool for multiplying and for quick mental arithmetic. From a(b + c) = ab + ac you build the products of binomials and three key algebraic identities — the square of a sum, the square of a difference, and the product of a sum and a difference. Area diagrams show why each identity is true, and you use them both to expand expressions and to compute numbers like 65², 998² and 53 × 47 in your head, while avoiding common expansion mistakes.
- Distributive property
- Multiplication spreads over addition: a × (b + c) = a×b + a×c. It is the rule behind every expansion of brackets, e.g. 6 × 13 = 6×10 + 6×3.
- Algebraic expression and terms
- A combination of numbers and letters joined by + or −, such as 3x + 5; each part (3x, 5) is a term, and the number multiplying a letter is its coefficient.
- Like terms
- Terms with exactly the same letters and powers, such as 3x and 5x, which can be added or subtracted: 3x + 5x − 2x = 6x.
- Expanding a product of binomials
- Each term of the first bracket multiplies each term of the second: (a + b)(c + d) = ac + ad + bc + bd.
- Square of a sum
- (a + b)² = a² + 2ab + b². The extra middle term 2ab is the area of the two rectangles when a square of side (a + b) is split up.
- Square of a difference
- (a − b)² = a² − 2ab + b². It is used to square numbers just below a round number, like 98² = (100 − 2)².
- Difference of two squares
- (a + b)(a − b) = a² − b²; the two middle products +ab and −ab cancel. This turns 53 × 47 into 50² − 3².
- Product (x + a)(x + b)
- Expands to x² + (a + b)x + ab, so the x-coefficient is the sum of the numbers and the constant is their product.
- Identities for fast arithmetic
- Writing a number as a sum or difference of easy parts lets an identity do the work: 65² = (60 + 5)² = 3600 + 600 + 25 = 4225.
- Area model
- A square of side (a + b) breaks into an a-square, a b-square and two a-by-b rectangles, which is a picture-proof that (a + b)² = a² + 2ab + b².
- Factorising with identities
- The identities read backwards let you factorise: x² − 9 = (x + 3)(x − 3) and x² + 10x + 25 = (x + 5)².
- Common expansion mistakes
- The frequent error (a + b)² = a² + b² drops the middle term; and distributing a minus changes the sign of every term inside the bracket.
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Start this chapter free →We Distribute, Yet Things Multiply — FAQs
What are the key concepts in Class 8 Mathematics We Distribute, Yet Things Multiply?+
This chapter turns the distributive property into a powerful tool for multiplying and for quick mental arithmetic. From a(b + c) = ab + ac you build the products of binomials and three key algebraic identities — the square of a sum, the square of a difference, and the product of a sum and a difference. Area diagrams show why each identity is true, and you use them both to expand expressions and to compute numbers like 65², 998² and 53 × 47 in your head, while avoiding common expansion mistakes. Key ideas include Distributive property, Algebraic expression and terms, Like terms, Expanding a product of binomials, Square of a sum, Square of a difference.
What does Class 8 Mathematics Chapter 6 (We Distribute, Yet Things Multiply) cover on XamBaaz?+
It has 72 NCERT-based MCQs on "We Distribute, Yet Things Multiply": 24 Easy, 24 Medium and 24 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams.
Are these "We Distribute, Yet Things Multiply" questions free to practise?+
Yes. Sign in with Google to practise "We Distribute, Yet Things Multiply" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 8 till 31 March; on 1 April your account moves up to Class 9 and the rest of your year carries over. No chapter is charged separately.
How should I revise "We Distribute, Yet Things Multiply" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "We Distribute, Yet Things Multiply" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "We Distribute, Yet Things Multiply" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from We Distribute, Yet Things Multiply (Class 8 Mathematics)?+
The questions that matter most test Distributive property, Algebraic expression and terms, Like terms, Expanding a product of binomials, Square of a sum, Square of a difference. This page shows 14 solved important MCQs with answers and explanations. Sign in to practise all 72 questions on the chapter as timed quizzes.
Is there an online quiz for We Distribute, Yet Things Multiply?+
Yes — Class 8 Mathematics We Distribute, Yet Things Multiply has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.