Important Questions Class 8 Maths Ganita Prakash – I Chapter 6 We Distribute, Yet Things Multiply

Short Questions

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

Answer: a(b+c)=ab+ac
Multiply a with each term inside the bracket.

2. Expand (a+1)(b+1).

Answer: ab+a+b+1
(a+1)(b+1)=ab+a+b+1

3. Expand $(a-b{)}^2$

Answer:

$a^2-2ab+b^2$ $$(a-b)(a-b)=a^2-ab-ab+b^2=a^2-2ab+b^2$$

4. Expand $(a+b)^2$.

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

5. Expand  $(a+b)(a-b)$.

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

6. Find $46^2$.

Solution:$${46}^2=(40+6{)}^2={40}^2+2(40)(6)+6^2$$

$$=1600+480+36=2116$$

7. Find $91^2$.

Solution:$${91}^2=(100-9{)}^2=10000-1800+81=8281$$

8. Expand $2(x+3)$

Answer: $2x+6$ $$2(x+3)=2x+6$$

9. Expand $(3+x)(x-2)$.

Answer: $x^2+x-6$ $$(3+x)(x-2)=3x-6+x^2-2x=x^2+x-6$$

10. Find $98 \times 102$

Answer:

$$(100-2)(100+2)={100}^2-2^2=10000-4=9996$$

Long Question

1. Expand $(2x+5)^2$.

Solution:
Using identity:$$(a+b{)}^2=a^2+2ab+b^2$$

Here $a=2x,\ b=5$ $$(2x+5{)}^2=(2x{)}^2+2(2x)(5)+5^2$$

$$(2x+5)^2=(2x)^2+2(2x)(5)+5^2$$ $$=4x^2+20x+25$$

2. Expand $(3a-4b)^2$.

Solution:
Using identity:

$$(a-b{)}^2=a^2-2ab+b^2$$

$$(a-b)^2=a^2-2ab+b^2$$ $$(3a-4b{)}^2=(3a{)}^2-2(3a)(4b)+(4b{)}^2$$

$$(3a-4b)^2=(3a)^2-2(3a)(4b)+(4b)^2$$ $$=9a^2-24ab+16b^2$$

3. Find $397 \times 403$.

Solution:$$397=400-3,403=400+3$$

Using:

$$(a-b)(a+b)=a^2-b^2$$

$$(a-b)(a+b)=a^2-b^2$$ $$(400-3)(400+3)={400}^2-3^2$$

$$(400-3)(400+3)=400^2-3^2$$ $$=160000-9=159991$$

4. Expand $(x+4)(x+7)$.

Solution:$$(x+4)(x+7)=x(x+7)+4(x+7)$$

$$=x^2+7x+4x+28$$

$$=x^2+11x+28$$

5. Find $145^2$.

Solution:$$145^2=(100+45)^2$$

$$=100^2+2(100)(45)+45^2$$

$$=10000+9000+2025$$

$$=21025$$