DAV Class 8 Maths Chapter 7 Worksheet 2 Solutions

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The DAV Class 8 Maths Solutions and DAV Class 8 Maths Chapter 7 Worksheet 2 Solutions of Algebraic Identities offer comprehensive answers to textbook questions.

DAV Class 8 Maths Ch 7 WS 2 Solutions

Question 1.
Find the following by using identity-II:

(i) (x – 7)2
Solution:
(x – 7)2 = x2 – 2 × x × 7 + (7)2
= x2 – 14x + 49

(ii) (5a – 4b)2
Solution:
(5a – 4b)2 = (5a)2 – 2 × 5a × 4b + (4b)2
= 25a2 – 40ab + 16b2

(iii) \(\left(\frac{7 x}{4}-\frac{2 y}{3}\right)^2\)
Solution:
\(\left(\frac{7 x}{4}-\frac{2 y}{3}\right)^2\)
= \(\left(\frac{7 x}{4}\right)^2-2\left(\frac{7 x}{4}\right)\left(\frac{2 y}{3}\right)+\left(\frac{2 y}{3}\right)^2\)
= \(\frac{49}{16} x^2-\frac{7}{3} x y+\frac{4 y^2}{9}\)

(iv) (8mn – 3pq)2
Solution:
(8mn – 3pq)2 = (8mn)2 – 2 × 8mn × 3pq + (3pq)2
= 64m2n2 – 48mn pq + 9 p2q2

(v) (0.1x – 0.5y)2
Solution:
(0.1x)2 – 2 × 0.1x × 0.5y + (0.5y)2
= 0.01x2 – 0.1x + 0.25y2

(vi) (a2 – b2)2
Solution:
= (a2)2 – 2a2b2 + (b2)2
= a4 + 2a2b2 + b4.

DAV Class 8 Maths Chapter 7 Worksheet 2 Solutions

Question 2.
Evaluate the following by using identity-II:

(i) (48)2
Solution:
(48)2 = (50 – 2)2
= (50)2 – 2 × 50 × 2 + (2)2
= 2500 – 200 + 4
= 2504 – 200
= 2304.

(ii) (9.9)2
Solution:
(9.9)2 = (10 – 0.1)2
= (10)2 – 2 × 10 × 0.1 + (0.1)2
= 100 – 2 + 0.01
= 100.01 – 2
= 98.01

(iii) (299)2
Solution:
(299)2 = (300 – 1)2
= (300)2 – 2 × 300 × 1 + (1)2
= 90000 – 600 + 1
= 90001 – 600
= 89401

(iv) (98)2
Solution:
(98)2 = (100 – 2)2
= (100)2 – 2 × 100 × 2 + (2)2
= 10000 – 400 + 4
= 10004 – 400
= 9604

DAV Class 8 Maths Chapter 7 Worksheet 2 Solutions

(v) (87)2
Solution:
(87)2 = (90 – 3)2
= (90)2 – 2 × 90 × 3 + (3)2
= 8100 – 540 + 9
= 8109 – 540
= 7569.

(vi) (19.9)2
Solution:
(19.9)2 = (20 – 0.1)2
= (20)2 – 2 × 20 × 0.1 + (0.1)2
= 400 – 4 + 0.01
= 400.01 – 4
= 396.01