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We Distribute, Yet Things Multiply – Class 8 Mathematics notes, important questions and MCQs

NCERT Class 8 Mathematics, chapter 6. Notes, key terms, important questions with answers and MCQs.

Chapter overview

The distributive property, a(b + c) = ab + ac, lets us multiply expressions and do quick mental calculations. It also gives the standard algebraic identities.

Distributive property

a(b + c) = ab + ac and a(b − c) = ab − ac.
Mental maths: 23 × 101 = 23 × 100 + 23 = 2323.
Multiplying binomials: (a + b)(c + d) = ac + ad + bc + bd.

Identities

(a + b)² = a² + 2ab + b².
(a − b)² = a² − 2ab + b².
(a + b)(a − b) = a² − b².

Key terms

Distributive property: multiplication spreads over addition or subtraction
Binomial: an expression with two terms
Identity: an equality true for every value of the variable, e.g. (a + b)² = a² + 2ab + b²

Formulas

(a + b)(a − b) = a² − b²
(x + a)(x + b) = x² + (a + b)x + ab

Important questions with answers

Expand (2a − 3)².2 marks

4a² − 12a + 9.

Find 52 × 48 using (a + b)(a − b) = a² − b².3 marks

(50 + 2)(50 − 2) = 2500 − 4 = 2,496.

Show that the area of a square of side (a + b) can be split into a², 2ab and b², and use (a + b)² to find 105². Also expand (x + 2)(x² − 2x + 4).5 marks

A square of side a + b divides into a square of side a (area a²), a square of side b (b²) and two rectangles a × b (2ab), so (a + b)² = a² + 2ab + b². 105² = (100 + 5)² = 10,000 + 1,000 + 25 = 11,025. (x + 2)(x² − 2x + 4) = x³ − 2x² + 4x + 2x² − 4x + 8 = x³ + 8.

Quick revision

Every term in the first bracket multiplies every term in the second.
(a + b)² ≠ a² + b².
Identities make mental calculation fast.

Exam tips

Write each step when expanding to avoid sign errors.
Use a² − b² for products like 49 × 51 = 50² − 1² = 2499.

Practice MCQs

5(x + 3) equals
1. 5x + 3
2. 5x + 8
3. x + 15
4. 5x + 15
Show answer
Answer: (d) 5x + 15. Multiply both terms.
12 × 11 using distribution, 12 × (10 + 1) =
1. 122
2. 121
3. 132
4. 112
Show answer
Answer: (c) 132. 120 + 12.
(x + 4)(x + 2) equals
1. x² + 6x + 6
2. x² + 8x + 6
3. x² + 6x + 8
4. x² + 2x + 8
Show answer
Answer: (c) x² + 6x + 8. x² + (4 + 2)x + 8.
98 × 102 equals
1. 10004
2. 9994
3. 9996
4. 9999
Show answer
Answer: (c) 9996. 100² − 2² = 9996.
(x + 5)(x + 3) equals
1. 2x + 8
2. x² + 15x + 8
3. x² + 8x + 8
4. x² + 8x + 15
Show answer
Answer: (d) x² + 8x + 15. Distribute.
(2a − 3b)² equals
1. 4a² − 9b²
2. 4a² − 12ab + 9b²
3. 4a² + 12ab + 9b²
4. 2a² − 6ab + 3b²
Show answer
Answer: (b) 4a² − 12ab + 9b². (a − b)² pattern.
The value of 47² − 53² is
1. −600
2. 600
3. −36
4. 100
Show answer
Answer: (a) −600. (47 + 53)(47 − 53) = 100 × (−6).
Using an identity, 98² equals
1. 9,404
2. 9,804
3. 9,604
4. 9,996
Show answer
Answer: (c) 9,604. (100 − 2)² = 10000 − 400 + 4.

All chapters of Class 8 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.