Express the following expression in reduced form. x 2 - 3 x + 2 x 2 - 1

Given expression is x 2 - 3 x + 2 x 2 - 1 . . . . i We need to find the reduced form of the above algebraic expression. First let us consider the numerator of the given algebraic expression that is x 2 - 3 x + 2 . . . 1 . Using the middle term splitting method we factorise 1 x 2 - 3 x + 2 = x 2 - 2 + 1 x + 2 = x 2 - 2 x - x + 2 = x x - 2 - 1 x - 2 = x - 2 x - 1 . . . . 2 Now consider the denominator of the algebraic expression that is x 2 - 1 = x - 1 x + 1 ∵ a 2 - b 2 = a + b a - b . . . 3 Using 2 , 3 in i we get: x 2 - 3 x + 2 x 2 - 1 = x - 1 x - 2 x - 1 x + 1 = x - 2 x + 1

Express the following expression in reduced form. a + 1 a - 2 × a 2 - a - 2 a 2 + a

Given expression is a + 1 a - 2 × a 2 - a - 2 a 2 + a . . . 1 We need to find the reduced form of the above algebraic expression. Consider the algebraic expression a 2 - a - 2 . Now, using the middle term splitting method let us factorise the above algebraic expression. That is, a 2 - a - 2 = a 2 - 2 - 1 a - 2 = a 2 - 2 a + a - 2 = a a - 2 + 1 a - 2 = a - 2 a + 1 . . . 2 Now, consider the algebraic expression a 2 + a = a a + 1 . . . 3 (by taking the common factors we factorise here) Now, using 2 , 3 in 1 we get: a + 1 a - 2 × a 2 - a - 2 a 2 + a = a + 1 a - 2 × a - 2 a + 1 a a + 1 = a + 1 a

Express the following expression in reduced form. p 3 + q 3 p 2 - q 2 ÷ p - q p + q

Given expression is p 3 + q 3 p 2 - q 2 ÷ p - q p + q . . . 1 We need to find the reduced form of the above algebraic expression. Consider the algebraic expression p 3 + q 3 = p + q p 2 - p q + q 2 . . . 2 (using the identity a 3 + b 3 = a + b a 2 - a b + b 2 ) Now, consider the algebraic identity in the algebraic expression p 2 - q 2 we get: p 2 - q 2 = p - q p + q . . . 3 Using 2 , 3 in 1 we get: p 3 + q 3 p 2 - q 2 ÷ p - q p + q = p + q p 2 - p q + q 2 p + q p - q × p + q p - q = p + q p 2 - p q + q 2 p - q 2

Express the following expression in reduced form. x 2 - x - 6 x 2 + 4 x - 5 × x 2 + 6 x + 5 x 2 - 4 x + 3

Given expression is x 2 - x - 6 x 2 + 4 x - 5 × x 2 + 6 x + 5 x 2 - 4 x + 3 . . . . 1 We need to find the reduced form of the above algebraic expression. Here each of the algebraic expression is quadratic, so we need to find the factors of each of the algebraic expression. Now, we will factorise each of these expressions by using the middle term splitting method to find the factors. x 2 - x - 6 = x 2 - 3 - 2 x - 6 = x 2 - 3 x + 2 x - 6 = x x - 3 + 2 x - 3 = x - 3 x + 2 . . . . 2 x 2 + 4 x - 5 = x 2 + 5 - 1 x - 5 = x 2 + 5 x - x - 5 = x x + 5 - 1 x + 5 = x + 5 x - 1 . . . . 3 x 2 + 6 x + 5 = x 2 + 5 + 1 x + 5 = x 2 + 5 x + x + 5 = x x + 5 + 1 x + 5 = x + 5 x + 1 . . . 4 x 2 - 4 x + 3 = x 2 - 3 + 1 x + 3 = x 2 - 3 x - x + 3 = x x - 3 - 1 x - 3 = x - 3 x - 1 . . . 5 Using 2 , 3 , 4 , 5 in 1 we get: ⇒ x 2 - x - 6 x 2 + 4 x - 5 × x 2 + 6 x + 5 x 2 - 4 x + 3 = x - 3 x + 2 x + 5 x - 1 × x + 5 x + 1 x - 3 x - 1 ⇒ x 2 - x - 6 x 2 + 4 x - 5 × x 2 + 6 x + 5 x 2 - 4 x + 3 = x + 2 x + 1 x - 1 2

Express the following expression in reduced form. a 2 - a b + b 2 a 2 + a b ÷ a 3 + b 3 a 2 - b 2

Given expression is a 2 - a b + b 2 a 2 + a b ÷ a 3 + b 3 a 2 - b 2 . . 1 We need to find the reduced form of the above algebraic expression. Consider the algebraic expression separately to factorise it. First consider a 2 + a b = a a + b . . . 2 (since a is the common factor) Next using the algebraic identity in a 3 + b 3 we get: a 3 + b 3 = a + b a 2 - a b + b 2 . . . 3 At last use the algebraic identity in a 2 - b 2 we get: a 2 - b 2 = a - b a + b . . . . 4 Using 2 , 3 , 4 in 1 , we get: a 2 - a b + b 2 a 2 + a b ÷ a 3 + b 3 a 2 - b 2 = a 2 - a b + b 2 a 2 + a b × a 2 - b 2 a 3 + b 3 = a 2 - a b + b 2 a a + b × a - b a + b a + b a 2 - a b + b 2 = a - b a a + b = a - b a 2 + a b Hence, a 2 - a b + b 2 a 2 + a b ÷ a 3 + b 3 a 2 - b 2 = a - b a 2 + a b

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Ganitprabha (MATHEMATICS TEXT BOOK) Class 8>Chapter 15 - Simplification of Algebraic Expression>Let's work out - 15

West Bengal Board Solutions for Chapter: Simplification of Algebraic Expression, Exercise 4: Let's work out - 15

Author:West Bengal Board

West Bengal Board Mathematics Solutions for Exercise - West Bengal Board Solutions for Chapter: Simplification of Algebraic Expression, Exercise 4: Let's work out - 15

Attempt the practice questions on Chapter 15: Simplification of Algebraic Expression, Exercise 4: Let's work out - 15 with hints and solutions to strengthen your understanding. Ganitprabha (MATHEMATICS TEXT BOOK) Class 8 solutions are prepared by Experienced Embibe Experts.