# DAV Class 8 Maths Chapter 7 Worksheet 3 Solutions

The DAV Class 8 Maths Solutions and DAV Class 8 Maths Chapter 7 Worksheet 3 Solutions of Algebraic Identities offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 7 WS 3 Solutions

Question 1.
Find the following products using identity – III:

(i) (2x + 7y) (2x – 7y)
Solution:
(2x + 7y) (2x – 7y) = (2x)2 – (7y)2
= 4x2 – 49y2

(ii) (5ab – 8c) (5ab + 8c)
Solution:
(5ab – 8c) (5ab + 8c) = (5ab)2 – (8c)2
= 25a2b2 – 64c2

(iii) (4p2 + q2) (4p2 – q2)
Solution:
(4p2 + q2) (4p2 – q2) = (4p2)2 – (q2)2
= 16p4 – q4

(iv) $$\left(\frac{x}{3}-\frac{y}{2}\right)\left(\frac{x}{3}+\frac{y}{2}\right)$$
Solution:
$$\left(\frac{x}{3}-\frac{y}{2}\right)\left(\frac{x}{3}+\frac{y}{2}\right)$$
= $$\left(\frac{x}{3}\right)^2-\left(\frac{y}{2}\right)^2$$
= $$\frac{x^2}{9}-\frac{y^2}{4}$$

(v) (0.1m – 0.2n) (0.1m + 0.2n)
Solution:
(0.1m – 0.2n) (0.1m + 0.2n) = (0.1m)2 – (0.2n)2
= 0.01m2 – 0.04n2

(vi) (a3 + b3) (a3 – b3)
Solution:
(a3 + b3) (a3 – b3) = (a3)2 – (b3)2
= a6 – b6

Question 2.
Evaluate the following by using identity — III:

(i) (81)2 – (19)2
Solution:
(81)2 – (19)2 = (81 + 19) (81 – 19)
= 100 × 62
= 6200

(ii) (290)2 – (210)2
Solution:
(290)2 – (210)2 = (290 + 210) (290 – 210)
= 500 × 80
= 40000

(iii) (58)2 – (12)2
Solution
(58)2 – (12)2 = (58 + 12) (58 – 12)
= 70 × 46
= 3220

(iv) (176)2 – (24)2
Solution:
(176)2 – (24)2
= (176 + 24) (176 – 24)
= 200 × 152
= 30400

(v) (367)2 – (33)2
Solution:
(367)2 – (33)2 = (367 + 33) (367 – 33)
= 400 × 34
= 133600

(vi) (545)2 – (445)2
Solution:
(545)2 – (445)2 = (545 + 445) (545 – 445)
= 990 × 100
= 99000

Question 3.
Simplify the following products by expressing these as difference of two squares:

(i) 107 × 93
Solution:
107 × 93 = (100 + 7) (100 – 7)
=(100)2 – (7)2
= 10000 – 49
=9951

(ii) 211 × 189
Solution:
211 × 189 = (200 + 11) (200 – 11)
= (200)2 – (11)2
= 40000 – 121
= 39879

(iii) 195 × 205
Solution:
195 × 205 = (200 – 5) (200 + 5)
= (200)2 – (5)2
= 40000 – 25
= 39975

(iv) 308 × 292
Solution:
308 × 292 = (300 + 8) (300 – 8)
= (300)2 – (8)2
= 90000 – 64
= 89936

(v) 12.4 × 11.6
Solution:
12.4 × 11.6 = (12 + 0.4) (12 – 0.4)
= (12)2 – (0.4)2
= 144 – 0.16
= 143.84

(vi) 30.9 × 29.1
Solution:
30.9 × 29.1 = (30 + 0.9) (30 – 0.9)
= (30)2 – (0.9)2
= 900 – 0.81
= 899.19