Write down the square of the expression 5 p - 1 4 q .

Given: 5 p - 1 4 q The square of 5 p - 1 4 q is given by 5 p - 1 4 q 2 . We know that, a - b 2 = a 2 - 2 a b + b 2 Here, a = 5 p and b = 1 4 q So, substituting, ⇒ 5 p - 1 4 q 2 = 5 p 2 - 2 5 p 1 4 q + 1 4 q 2 ⇒ 5 p - 1 4 q 2 = 25 p 2 - 5 p 2 q + 1 16 q 2 Hence, 5 p - 1 4 q 2 = 25 p 2 - 5 p 2 q + 1 16 q 2

Expand 1 3 - 5 x 1 3 + 5 x .

We need to expand 1 3 - 5 x 1 3 + 5 x . We know the identity, ( a + b ) ( a - b ) = a 2 - b 2 Here, a = 1 3 and b = 5 x Substituting the values, ⇒ 1 3 - 5 x 1 3 + 5 x = 1 3 2 - 5 x 2 ⇒ 1 3 - 5 x 1 3 + 5 x = 1 9 - 25 x 2 Hence, 1 3 - 5 x 1 3 + 5 x = 1 9 - 25 x 2

Expand a 4 - 1 5 y a 4 + 1 5 y

We need to expand a 4 - 1 5 y a 4 + 1 5 y . We know the identity, ( m + n ) ( m - n ) = m 2 - n 2 Here, m = a 4 and n = 1 5 y Substituting the values, ⇒ a 4 - 1 5 y a 4 + 1 5 y = a 4 2 - 1 5 y 2 ⇒ a 4 - 1 5 y a 4 + 1 5 y = a 8 - 1 25 y 2 Hence, a 4 - 1 5 y a 4 + 1 5 y = a 8 - 1 25 y 2

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ICSE Mathematics>Algebra>Chapter 3 - Expansions>Exercise

O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 1: Exercise

Author:O P Malhotra, S K Gupta & Anubhuti Gangal

O P Malhotra Mathematics Solutions for Exercise - O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 1: Exercise

Attempt the practice questions from Exercise 1: Exercise with hints and solutions to strengthen your understanding. ICSE Mathematics solutions are prepared by Experienced Embibe Experts.