We Distribute Yet Things Multiply: Important Questions and Answers for Class 8

Important Questions on We Distribute Yet Things Multiply for Class 8 are available in this Maths article. Important Questions on We Distribute Yet Things Multiply for Class 8 are very useful to solve the problems easily. This article helps the students to know the key questions and answers about We Distribute Yet Things Multiply. We Distribute Yet Things Multiply covers division, factors, multiples, and their relationships, which we use in everyday calculations. Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination. 

Table of Contents

• Exercise 1.1: Distributive Property of Multiplication
• Exercise 1.2: Algebraic Expressions
• Exercise 1.3: Algebraic Identities
• Exercise 1.4: Applications of Distributive Property
• Tips for Understanding We Distribute Yet Things Multiply for Class 8
• Most Common Examination Questions (Board Exams)

Exercise 1.1: Distributive Property of Multiplication

Question 1: What is the distributive property of multiplication over addition?

Answer: The distributive property states:

a(b+c)=ab+ac

This means multiplication is distributed to each term inside the bracket.

Question 2: Use distributive property to solve: 24 × (10 + 2)

Answer:

Step 1: Multiply 24 by 10
24 × 10 = 240

Step 2: Multiply 24 by 2
24 × 2 = 48

Step 3: Add the results
240 + 48 = 288

Answer: 288

Question 3: Expand: 3(x + 5)

Answer:

Multiply 3 with each term inside the bracket.

3 × x = 3x
3 × 5 = 15

Answer: 3x + 15

Question 4: Expand: 7(a − 2)

Answer:

7 × a = 7a
7 × (−2) = −14

Answer: 7a − 14

Question 5: Find the value of: 15 × 101

Answer:

Using distributive property:

15 × (100 + 1)

= 15 × 100 + 15 × 1

= 1500 + 15

= 1515

Answer: 1515

Exercise 1.2: Algebraic Expressions

Question 1: What are like terms?

Answer:

Terms having the same variables and powers are called like terms.

Example:
3x and 5x

Question 2: Simplify: 4x + 3x

Answer:

Add the coefficients.

4x + 3x = 7x

Answer: 7x

Question 3: Simplify: 8a − 2a + 5

Answer:

8a − 2a = 6a

So the expression becomes:

6a + 5

Answer: 6a + 5

Question 4: Expand: 5(p + q)

Answer:

5 × p = 5p
5 × q = 5q

Answer: 5p + 5q

Question 5: Simplify: 10m + 7m − 4m

Answer:

10m + 7m = 17m

17m − 4m = 13m

Answer: 13m

Exercise 1.3: Algebraic Identities

Question 1: Write the identity for the square of a sum.

Answer:

a(b+c)=ab+ac

Question 2: Expand: (x + 3)²

Answer:

Using identity:

(x + 3)² = x² + 2(x)(3) + 3²

= x² + 6x + 9

Answer: x² + 6x + 9

Question 3: Write the identity for the difference of squares.

Answer:  (a+b)(a−b)=a2−b2

Question 4: Expand: (a − 5)²

Answer:

Using identity:

(a − 5)² = a² − 2(a)(5) + 5²

= a² − 10a + 25

Answer: a² − 10a + 25

Question 5: Find: (2x + 1)(2x − 1)

Answer:

Using identity:

(2x)² − (1)²

= 4x² − 1

Answer: 4x² − 1

Exercise 1.4: Applications of Distributive Property

Question 1: A teacher buys 25 notebooks costing ₹12 each. Find the total cost.

Answer:

Total cost = 25 × 12

= 25 × (10 + 2)

= 250 + 50

= 300

Answer: ₹300

Question 2: A box contains 15 rows of chocolates with 8 chocolates in each row. Find the total chocolates.

Answer:

15 × 8 = 120

Answer: 120 chocolates

Question 3: Find: 99 × 7

Answer:

99 × 7 = (100 − 1) × 7

= 700 − 7

= 693

Answer: 693

Question 4: A shopkeeper sells 18 pens at ₹15 each. Find the total amount.

Answer:

18 × 15

= 18 × (10 + 5)

= 180 + 90

= 270

Answer: ₹270

Question 5: Find: 52 × 11

Answer:

52 × (10 + 1)

= 520 + 52

= 572

Answer: 572

Tips for Understanding We Distribute Yet Things Multiply for Class 8

1. Learn distributive property carefully.

2. Practice algebraic expressions daily.

3. Remember algebraic identities using formulas.

4. Solve step-by-step problems regularly.

5. Revise identities before exams.

6. Practice simplifying expressions.

7. Avoid calculation mistakes in signs.

8. Write all multiplication steps clearly.

9. Solve previous year important questions.

10. Practice mental multiplication tricks.

Most Common Examination Questions (Board Exams)

1 – 2 Mark Questions (Very Frequently Asked)

Question 1: Expand: 2(a + 4)

Answer:

2a + 8

Question 2: Write the identity for: (a − b)²

Answer:

(a−b)2=a2−2ab+b2

Question 3: Simplify: 5x + 2x

Answer: 7x

Question 4: Find: 12 × 101

Answer:

12 × (100 + 1)

= 1200 + 12

= 1212

Answer: 1212

Question 5: What are like terms?

Answer:

Terms having the same variables and powers are called like terms.

3 – 4 Mark Questions (Frequently Asked)

Question 1: Expand: 4(x + 6)

Answer:

4 × x = 4x
4 × 6 = 24

Answer: 4x + 24

Question 2: Simplify: 7a + 5a − 3a

Answer:

7a + 5a = 12a

12a − 3a = 9a

Answer: 9a

Question 3: Expand: (y + 2)²

Answer:

(y + 2)² = y² + 2(y)(2) + 2²

= y² + 4y + 4

Answer: y² + 4y + 4

Question 4: Find: 49 × 11

Answer:

49 × (10 + 1)

= 490 + 49

= 539

Answer: 539

Question 5: Expand: (a + b)(a − b)

Answer:

a² − b²

5 – 6 Mark Questions (Less Frequent but Important)

Question 1: Explain distributive property with an example.

Answer:

The distributive property means multiplication can be distributed over addition.

Example:

6(4 + 2)

= 6 × 4 + 6 × 2

= 24 + 12

= 36

This method makes calculations easier.

Question 2: Expand and simplify: (2x + 3)²

Answer:

Using identity:

(2x + 3)²

= (2x)² + 2(2x)(3) + 3²

= 4x² + 12x + 9

Answer: 4x² + 12x + 9

Question 3: A shopkeeper buys 35 boxes with 12 chocolates in each box. Find the total chocolates using distributive property.

Answer:

35 × 12

= 35 × (10 + 2)

= 350 + 70

= 420

Answer: 420 chocolates

Question 4: Expand: (a − 4)(a + 4)

Answer:

Using identity:

a² − 4²

= a² − 16

Answer: a² − 16

Question 5: Explain algebraic identity with an example.

Answer: An algebraic identity is an equation that is true for all values of variables.

(a + b)² = a² + 2ab + b²

Let: a = 8, b = 3.5

Substituting the values:

(8 + 3.5)² = 8² + 2(8)(3.5) + 3.5²

11.5² = 64 + 56 + 12.25

132.25 = 132.25

Step-by-Step Expansion

(a + b)²

= a² + ab + ab + b²

= a² + 2ab + b²