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}

= 4x^{2} – 49y^{2}

(ii) (5ab – 8c) (5ab + 8c)

Solution:

(5ab – 8c) (5ab + 8c) = (5ab)^{2} – (8c)^{2}

= 25a^{2}b^{2} – 64c^{2}

(iii) (4p^{2} + q^{2}) (4p^{2} – q^{2})

Solution:

(4p^{2} + q^{2}) (4p^{2} – q^{2}) = (4p^{2})^{2} – (q^{2})^{2}

= 16p^{4} – q^{4}

(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}

= 0.01m^{2} – 0.04n^{2}

(vi) (a^{3} + b^{3}) (a^{3} – b^{3})

Solution:

(a^{3} + b^{3}) (a^{3} – b^{3}) = (a^{3})^{2} – (b^{3})^{2}

= a^{6} – b^{6}

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