We Distribute, Yet Things Multiply — Class 8 MCQs with Answers

We Distribute, Yet Things Multiply — important questions & MCQs with answers (Class 8 Mathematics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

1. Q1 of 6Easy

   The distributive property states that a × (b + c) equals:

   Aa×b + a×cBa×b × a×cCa + b × cDab + c
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   Answer: 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.

2. Q2 of 6Easy

   The identity for (a + b)² is:

   Aa² + b²Ba² + 2ab + b²Ca² − 2ab + b²D2a + 2b
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   Answer: 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.

3. Q3 of 6Medium

   Rahul writes (a + b)² = a² + b². What has he left out?

   Athe term b²Bthe middle term 2abCthe term a²Dnothing, it is correct
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   Answer: 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.

4. Q4 of 6Medium

   Using an identity, evaluate 104².

   A10816B10616C10800D11016
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   Answer: 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.

5. Q5 of 6Hard

   Expand (2x + 3y)².

   A4x² + 9y²B4x² + 12xy + 9y²C4x² + 6xy + 9y²D2x² + 12xy + 9y²
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   Answer: 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.

6. Q6 of 6Hard

   Evaluate 1002² using an identity.

   A1004004B1002004C1000404D1004040
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   Answer: 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.

We Distribute, Yet Things Multiply notes: key concepts (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.