Algebra becomes easier when students understand how numbers, variables, and expressions work together. CBSE Board Class 8 Maths Chapter 6 We Distribute, Yet Things Multiply from the Ganita Prakash textbook introduces students to important concepts like distributive property, multiplication of algebraic expressions, and algebraic identities.
These Class 8 Chapter 6 We Distribute, Yet Things Multiply Maths MCQs are designed to help students strengthen their conceptual understanding through application-based questions. Each question encourages logical thinking and helps students practise different methods of simplifying expressions.
Students can use these chapter-wise MCQs for quick revision, classroom tests, and improving their problem-solving speed. The questions include answers with explanations so learners can understand the correct approach instead of just memorising formulas.
For better preparation, students can explore more Class 8 MCQs covering different subjects and continue practising chapter-wise Class 8 Maths MCQs to build confidence in Mathematics.
Chapter 6 We Distribute, Yet Things Multiply MCQs with Answers and Explanation
Practice these challenging Class 8 Maths Chapter 6 We Distribute, Yet Things Multiply MCQs with Answers based on algebraic identities, distributive property, and multiplication of expressions. These questions follow the CBSE Ganita Prakash learning approach and help students build strong mathematical reasoning.
Q. The value of (x + 8)² − (x − 8)² is 320. Find the value of x.
A. 15
B. 20
C. 10
D. 25
Answer: C. 10
Explanation:
Using identity: (a + b)² − (a − b)² = 4ab
4 × x × 8 = 320
32x = 320, therefore x = 10.
Q. Simplify the expression (4a + 3)(4a − 3).
A. 16a² + 9
B. 8a² − 9
C. 16a² − 9
D. 4a² − 6
Answer: C. 16a² − 9
Explanation:
Using (a + b)(a − b) = a² − b²
(4a)² − 3² = 16a² − 9.
Q. What is the expanded form of (3x − 2y)²?
A. 9x² − 12xy + 4y²
B. 9x² + 12xy + 4y²
C. 6x² − 6xy + 2y²
D. 9x² − 4y²
Answer: A. 9x² − 12xy + 4y²
Explanation:
According to (a − b)² = a² − 2ab + b²,
(3x − 2y)² = 9x² − 12xy + 4y².
Q. Calculate 997 × 1003 using a suitable identity.
A. 999991
B. 999900
C. 1000009
D. 999009
Answer: A. 999991
Explanation:
997 × 1003 = (1000 − 3)(1000 + 3)
= 1000² − 3²
= 1000000 − 9 = 999991.
Q. If p + q = 16 and pq = 55, then find p² + q².
A. 146
B. 156
C. 166
D. 176
Answer: A. 146
Explanation:
(p + q)² = p² + q² + 2pq
256 = p² + q² + 110
p² + q² = 146.
Q. Expand (x + 6)(x + 8).
A. x² + 14x + 48
B. x² + 48x + 14
C. x² − 14x + 48
D. x² + 2x + 48
Answer: A. x² + 14x + 48
Explanation:
Using (x+a)(x+b)=x²+(a+b)x+ab
= x²+14x+48.
Q. Which option correctly represents the distributive law?
A. a(b+c)=ab+c
B. a(b+c)=a+b+c
C. a(b+c)=ab+ac
D. a(b−c)=ab+c
Answer: C. a(b+c)=ab+ac
Explanation:
The distributive property means multiplying the outside term with every term inside the bracket.
Q. Find the square of 106 using an algebraic identity.
A. 11236
B. 11136
C. 11036
D. 11336
Answer: A. 11236
Explanation:
106² = (100+6)²
=10000+1200+36
=11236.
Q. If (x − 9)(x + 9)=319, find the value of x².
A. 390
B. 400
C. 410
D. 420
Answer: B. 400
Explanation:
x² − 81 = 319
x² = 400.
Q. Expand (4m + 3n)².
A. 16m² + 24mn + 9n²
B. 16m² − 24mn + 9n²
C. 8m² + 12mn + 9n²
D. 16m² + 9n²
Answer: A. 16m² + 24mn + 9n²
Explanation:
Apply (a+b)²=a²+2ab+b².
Q. Which identity form can be used to solve 68 × 72 quickly?
A. 70² − 2²
B. 70² + 2²
C. 68² + 72²
D. 140² − 4²
Answer: A. 70² − 2²
Explanation:
68 × 72 = (70−2)(70+2), which follows a²−b².
Q. Simplify (5p − 6)(5p + 6).
A. 25p² + 36
B. 25p² − 36
C. 10p² − 12
D. 25p² − 30p
Answer: B. 25p² − 36
Explanation:
Using (a+b)(a−b)=a²−b².
Q. Write x² + 14x + 49 in identity form.
A. (x−7)²
B. (x+14)²
C. (x+7)²
D. (x−14)²
Answer: C. (x+7)²
Explanation:
The expression follows the identity a²+2ab+b².
Q. Simplify the expression 5x(3x + 4).
A. 15x² + 20x
B. 8x² + 20x
C. 15x² − 20x
D. 15x + 20
Answer: A. 15x² + 20x
Explanation:
Multiply 5x separately with both terms inside the bracket.
Q. Complete the identity: (a−b)² = a² + b² − ____
A. ab
B. a+b
C. 2ab
D. 4ab
Answer: C. 2ab
Explanation:
The correct identity is (a−b)²=a²−2ab+b².
Q. Find the value of 304 × 296.
A. 89984
B. 89990
C. 90016
D. 90000
Answer: A. 89984
Explanation:
(300+4)(300−4)
=90000−16
=89984.
Q. Expand (6x − 5)(6x + 5).
A. 36x² + 25
B. 12x² − 25
C. 36x² − 25
D. 6x² − 10
Answer: C. 36x² − 25
Explanation:
It follows the identity (a+b)(a−b)=a²−b².
Q. Find the coefficient of x in (x+9)(x+5).
A. 45
B. 9
C. 14
D. 5
Answer: C. 14
Explanation:
Expansion gives x²+14x+45, so coefficient of x is 14.
Q. Which identity is suitable for calculating 98²?
A. (100−2)²
B. (100+2)²
C. 100²−2²
D. 98×100
Answer: A. (100−2)²
Explanation:
98 is close to 100, so this identity makes calculation easier.
Q. Simplify (x−5)² + 10x.
A. x²+25
B. x²−25
C. x²+10
D. x²−10x
Answer: A. x²+25
Explanation:
x²−10x+25+10x = x²+25.
Q. Expand (9+a)(9−a).
A. 81+a²
B. a²−81
C. 81−a²
D. 18−a²
Answer: C. 81−a²
Explanation:
Using (x+y)(x−y)=x²−y².
Q. Find the value of 59² using identity.
A. 3481
B. 3581
C. 3381
D. 3601
Answer: A. 3481
Explanation:
59²=(60−1)²
=3600−120+1=3481.
Q. Find the middle term after expanding (x+13)².
A. 13x
B. 26x
C. 169x
D. x²
Answer: B. 26x
Explanation:
Middle term = 2 × x × 13 = 26x.
Q. Which identity helps in solving 84 × 76 easily?
A. (a+b)²
B. a(b+c)
C. (a+b)(a−b)
D. (a−b)²
Answer: C. (a+b)(a−b)
Explanation:
84×76=(80+4)(80−4).
Q. If x+y=30 and x−y=4, find x²−y².
A. 90
B. 100
C. 120
D. 150
Answer: C. 120
Explanation:
x²−y²=(x+y)(x−y)=30×4=120.
Q. Simplify (2a+7b)(2a−7b).
A. 4a²−49b²
B. 4a²+49b²
C. 2a²−14b²
D. 14ab
Answer: A. 4a²−49b²
Explanation:
Use the difference of squares identity.
Q. Simplify: (x+6)² − 12x
A. x²+36
B. x²−36
C. x²+12
D. x²−12
Answer: A. x²+36
Explanation:
x²+12x+36−12x = x²+36.
Q. Expand (y−8)(y−4).
A. y²−12y+32
B. y²+12y+32
C. y²−32
D. y²−4y+32
Answer: A. y²−12y+32
Explanation:
Multiply the expressions using distributive property.
Q. Calculate 1005² − 5² using identity.
A. 1010000
B. 1000000
C. 1015000
D. 1005000
Answer: A. 1010000
Explanation:
a²−b²=(a+b)(a−b)
=1010×1000=1010000.
Q. Algebraic identities are mainly used to:
A. Make expressions longer
B. Remove all numbers from expressions
C. Simplify calculations quickly
D. Avoid mathematical rules
Answer: C. Simplify calculations quickly
Explanation:
Algebraic identities help solve multiplication and expressions in a faster and easier way.
Chapter 6 We Distribute, Yet Things Multiply At a Glance
| Chapter Details | Information |
|---|---|
| Class | 8 |
| Subject | Mathematics |
| Board | CBSE |
| Book | Ganita Prakash |
| Chapter Number | Chapter 6 |
| Chapter Name | We Distribute, Yet Things Multiply |
| Main Concepts | Distributive Property, Algebraic Expressions, Algebraic Identities |
| Practice Type | MCQs with Answers |
| Difficulty Level | Medium to Advanced |
Important Concepts From Chapter 6 We Distribute, Yet Things Multiply
Distributive Property:
The distributive property explains how multiplication works with addition or subtraction inside brackets. It helps students simplify calculations and expand algebraic expressions.
Example:
a(b + c) = ab + ac
This concept is useful for solving both numerical and algebra-based problems quickly.
Multiplication of Algebraic Expressions:
Algebraic multiplication involves multiplying variables, constants, and terms correctly. Students learn how to open brackets, multiply expressions, and combine like terms to get simplified answers.
This concept builds the foundation for advanced algebra topics.
Algebraic Identities:
Algebraic identities are standard formulas that help solve expressions faster.
Important identities:
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a + b)(a - b) = a² - b²
Understanding these identities helps students solve complex questions easily.
Using Identities for Smart Calculations:
Algebraic identities are also useful for finding squares and products of large numbers without lengthy multiplication.
Examples:
102² = (100 + 2)²
98 × 102 = (100 - 2)(100 + 2)
This improves speed and accuracy during exams.
How to Score Better in Chapter 6 We Distribute, Yet Things Multiply MCQs
To perform better in this chapter:
- Understand the meaning behind each algebraic identity.
- Do not only memorise formulas; practice their applications.
- Carefully check positive and negative signs while expanding.
- Solve different types of expression-based questions.
- Practice calculation tricks using identities.
- Review mistakes and understand the correct method.
Strong practice of Chapter 6 MCQs helps improve algebra confidence and prepares students for higher-level Maths.
