Find the product of 25 x 2 1 - 1 5 x . Verify the result for x = - 2

Given, 25 x 2 1 - 1 5 x The like terms are terms that have the same variables and powers. Arrange the constant terms and variables and multiply the like terms. = 25 x 2 1 - 1 5 x = 25 x 2 - 31 5 x 3 = 25 x 2 - 5 x 3 When, x = - 2 we have, L H S ⇒ 25 x 2 1 - 1 5 x = 25 - 2 2 1 - 1 5 - 2 = 100 1 - 4 5 = 20 R H S ⇒ 25 x 2 - 5 x 3 = 25 - 2 2 - 5 - 2 3 = 25 4 - 5 4 = 100 - 20 = 80 Thus, L H S ≠ R H S Hence, the required answer is obtained.

Simplify the following. 1 2 x 3 y 3 - z 3 + 1 2 y 3 z 3 - x 3 + 1 2 z 3 x 3 - y 3

Given, 1 2 x 3 y 3 - z 3 + 1 2 y 3 z 3 - x 3 + 1 2 z 3 x 3 - y 3 A binomial is defined as an algebraic expression that has two terms connected by a plus or a minus sign. Multiplying binomials is similar to the multiplication of two whole numbers or fractions. Thus, ⇒ 1 2 x 3 y 3 - z 3 + 1 2 y 3 z 3 - x 3 + 1 2 z 3 x 3 - y 3 = 1 2 x 3 y 3 - 1 2 x 3 z 3 + 1 2 y 3 z 3 - 1 2 y 3 x 3 + 1 2 z 3 x 3 - 1 2 z 3 y 3 = 0 Hence, the required answer is obtained.

Simplify the following. 3 2 x 2 1 3 - x 2 + 3 x 1 2 x 3 - 1 3 x + 9 5 x 2 x 3 - x

Given, 3 2 x 2 1 3 - x 2 + 3 x 1 2 x 3 - 1 3 x + 9 5 x 2 x 3 - x A binomial is defined as an algebraic expression that has two terms connected by a plus or a minus sign. Multiplying binomials is similar to the multiplication of two whole numbers or fractions. Thus, ⇒ 3 2 x 2 1 3 - x 2 + 3 x 1 2 x 3 - 1 3 x + 9 5 x 2 x 3 - x = 3 2 × 1 3 x 2 - 3 2 x 4 + 3 2 x 4 - 1 x 2 + 9 5 x 5 - 9 5 x 3 = 9 5 x 5 - 9 5 x 3 - x 2 2 Hence, the required answer is obtained.

Simplify the following. 1 3 x x 2 - x 3 + 2 3 x 2 x 3 - x + 4 3 x 3 x - x 2

Given, 1 3 x x 2 - x 3 + 2 3 x 2 x 3 - x + 4 3 x 3 x - x 2 A binomial is defined as an algebraic expression that has two terms connected by a plus or a minus sign. Multiplying binomials is similar to the multiplication of two whole numbers or fractions. Thus, ⇒ 1 3 x x 2 - x 3 + 2 3 x 2 x 3 - x + 4 3 x 3 x - x 2 = 1 3 x 3 - 1 3 x 4 + 2 3 x 5 - 2 3 x 3 + 4 3 x 4 - 4 3 x 5 = 1 3 - x 3 + 3 x 4 - 2 x 5 Hence, the required answer is obtained.

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Maths Hub (ICSE)>Chapter 6 - Algebraic Expressions and Identities>CHECK POINT

S Purkayastha Solutions for Chapter: Algebraic Expressions and Identities, Exercise 3: CHECK POINT

Author:S Purkayastha

S Purkayastha Mathematics Solutions for Exercise - S Purkayastha Solutions for Chapter: Algebraic Expressions and Identities, Exercise 3: CHECK POINT

Attempt the free practice questions on Chapter 6: Algebraic Expressions and Identities, Exercise 3: CHECK POINT with hints and solutions to strengthen your understanding. Maths Hub (ICSE) solutions are prepared by Experienced Embibe Experts.