Important Questions and Answers for Class 8 Maths Chapter 6 We Distribute Yet Things Multiply 2025-26

1. Multiple choice questions.

1. Which of the following correctly represents the distributive property of multiplication over addition?

• (a) $a+b = b+a$
• (b) $a(b+c)=ab+ac$
• (c) $a(b-c)=ab-c$
• (d) $ab=ba$

Answer: (b) $a(b+c)=ab+ac$

2. If you increase both factors in the product $ab$ by $1$, what is the increase in the product?

• (a) $a+b$
• (b) $a+b+1$
• (c) $ab+1$
• (d) $2ab$

Answer: (b) $a+b+1$

3. Which of the following is the correct expansion for $(a - b)^2$?

• (a) $a^2 + 2ab + b^2$
• (b) $a^2 + b^2 - 2ab$
• (c) $a^2 - 2ab + b^2$
• (d) $a^2 - b^2$

Answer: (c) $a^2 - 2ab + b^2$

4. The value of $(a+b)(a-b)$ is:

• (a) $a^2+b^2$
• (b) $a^2-b^2$
• (c) $ab+ba$
• (d) $2ab$

Answer: (b) $a^2-b^2$

2. Very Short Answer (VSA).

1. What is the distributive property of multiplication over addition?

Answer: The distributive property states that $a(b+c) = ab + ac$, where $a$, $b$, $c$ are numbers.

2. Write the expansion of $(a+b)^2$.

Answer: $(a+b)^2 = a^2 + 2ab + b^2$.

3. State what an algebraic identity is.

Answer: An algebraic identity is an equation that holds true for any values of the variables involved.

4. What is meant by like terms in algebra?

Answer: Like terms are terms that have exactly the same variables and degrees but may have different coefficients.

5. Expand $(a-b)(a+b)$.

Answer: $(a-b)(a+b) = a^2 - b^2$.

3. Short Answer Questions.

1. Using the distributive property, explain how to quickly calculate $56 \times 101$.

Answer: Using the distributive property, 

$56 \times 101 = 56 \times (100+1) = 56 \times 100 + 56 \times 1 = 5600 + 56 = 5656$.

2. How does the distributive property help to expand $(3a/2)(a - b + 1/5)$?

Answer: By the distributive property: 

$(3a/2)(a - b + 1/5) = (3a/2)a - (3a/2)b + (3a/2)\times(1/5) = (3/2)a^2 - (3/2)ab + (3/10)a$.

3. If the product $ab$ remains unchanged when $a$ is increased by $2$ and $b$ is decreased by $4$, give an example of such a pair $(a, b)$.

Answer: Let $a=6$ and $b=8$. $ab = 48$. If $a$ becomes $8$ and $b$ becomes $4$, then $8 \times 4 = 32$, so not unchanged. Try $a=9$, $b=6$: $ab=54$; $11\times2=22$. Let's use $a=3$, $b=6$: $3\times6=18$; $5\times2=10$. Adjust for $a=2$, $b=4$, $ab=8$; $4\times0=0$. The only way both numbers satisfy $ab=(a+2)(b-4)$ is if $2ab+2b-4a-8=ab \Rightarrow ab-2b+4a+8=0$, which usually does not have integer solutions. A valid example is $a=0$, $b=0$, both products give $0$.

4. Why does the identity $(a+b)(a-b) = a^2 - b^2$ work for all numbers?

Answer: When expanded, $(a+b)(a-b) = a^2 - ab + ba - b^2$; since $-ab+ba=0$, it simplifies to $a^2-b^2$ for all $a$ and $b$.

5. Describe a quick way to multiply a number by $11$ using distributivity.

Answer: To multiply any number by $11$, add each digit to its neighbor and write down the results, carrying over as needed. For example, $248 \times 11 = 2$ $(2+4)$ $(4+8)$ $8 = 2\,6\,12\,8$, adjust for carry, final answer is $2728$.

4. True or False Questions.

1. The distributive property says $a(b+c) = ab + ac$ for all integers $a, b, c$.

Answer: True.

2. In the expression $(a+b)^2$, the middle term is always $ab$.

Answer: False.

3. $(a+b)^2 = a^2 + b^2 + 2ab$ is an algebraic identity.

Answer: True.

4. $(a-b)^2 = a^2 - b^2$.

Answer: False.

3. Fill in the Blanks Questions.

1. The expansion of $(a + b)(a + b)$ is __________.

Answer: $a^2 + 2ab + b^2$

2. $(a + b)(a - b) = $ __________.

Answer: $a^2 - b^2$

3. $(a - b)^2=$ __________.

Answer: $a^2 - 2ab + b^2$

4. In the distributive property, $a(b+c) = $ __________.

Answer: $ab + ac$

5. Like terms have identical __________ and __________.

Answer: variables; degrees

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