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} = x^{2} – 2 × x × 7 + (7)^{2}

= x^{2} – 14x + 49

(ii) (5a – 4b)^{2}

Solution:

(5a – 4b)^{2} = (5a)^{2} – 2 × 5a × 4b + (4b)^{2}

= 25a^{2} – 40ab + 16b^{2}

(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}

= 64m^{2}n^{2} – 48mn pq + 9 p^{2}q^{2}

(v) (0.1x – 0.5y)^{2}

Solution:

(0.1x)^{2} – 2 × 0.1x × 0.5y + (0.5y)^{2}

= 0.01x^{2} – 0.1x + 0.25y^{2}

(vi) (a^{2} – b^{2})^{2}

Solution:

= (a^{2})^{2} – 2a^{2}b^{2} + (b^{2})^{2}

= a^{4} + 2a^{2}b^{2} + b^{4}.

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

(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