Evaluate: x 3 - 2 x 2 + 5 × 4 x - 1

Given expression: x 3 - 2 x 2 + 5 × 4 x - 1 Using horizontal method, we have x 3 - 2 x 2 + 5 × 4 x - 1 = 4 x - 1 × x 3 - 2 x 2 + 5 = 4 x x 3 - 2 x 2 + 5 - 1 x 3 - 2 x 2 + 5 = 4 x 4 - 8 x 3 + 20 x - x 3 + 2 x 2 - 5 = 4 x 4 - 9 x 3 + 2 x 2 + 20 x - 5 ∴ x 3 - 2 x 2 + 5 × 4 x - 1 = 4 x 4 - 9 x 3 + 2 x 2 + 20 x - 5

Evaluate: 9 x 2 - x + 15 × x 2 - 3

Given expression: 9 x 2 - x + 15 × x 2 - 3 Using horizontal method, we have 9 x 2 - x + 15 × x 2 - 3 = x 2 - 3 × 9 x 2 - x + 15 = x 2 9 x 2 - x + 15 - 3 9 x 2 - x + 15 = 9 x 4 - x 3 + 15 x 2 - 27 x 2 + 3 x - 45 = 9 x 4 - x 3 - 12 x 2 + 3 x - 45 ∴ 9 x 2 - x + 15 × x 2 - 3 = 9 x 4 - x 3 - 12 x 2 + 3 x - 45

Evaluate: x 2 - 5 x + 8 × x 2 + 2

Given expression: x 2 - 5 x + 8 × x 2 + 2 Using horizontal method, we have x 2 - 5 x + 8 × x 2 + 2 = x 2 + 2 × x 2 - 5 x + 8 = x 2 x 2 - 5 x + 8 + 2 x 2 - 5 x + 8 = x 4 - 5 x 3 + 8 x 2 + 2 x 2 - 10 x + 16 = x 4 - 5 x 3 + 10 x 2 - 10 x + 16 ∴ x 2 - 5 x + 8 × x 2 + 2 = x 4 - 5 x 3 + 10 x 2 - 10 x + 16

Evaluate: x 3 - 5 x 2 + 3 x + 1 × x 2 - 3

Given expression: x 3 - 5 x 2 + 3 x + 1 × x 2 - 3 Using horizontal method, we have x 3 - 5 x 2 + 3 x + 1 × x 2 - 3 = x 2 - 3 × x 3 - 5 x 2 + 3 x + 1 = x 2 x 3 - 5 x 2 + 3 x + 1 - 3 x 3 - 5 x 2 + 3 x + 1 = x 5 - 5 x 4 + 3 x 3 + x 2 - 3 x 3 + 15 x 2 - 9 x - 3 = x 5 - 5 x 4 + 16 x 2 - 9 x - 3 ∴ x 3 - 5 x 2 + 3 x + 1 × x 2 - 3 = x 5 - 5 x 4 + 16 x 2 - 9 x - 3

Evaluate: 3 x + 2 y - 4 × x - y + 2

Given expression: 3 x + 2 y - 4 × x - y + 2 Using horizontal method, we have 3 x + 2 y - 4 × x - y + 2 = 3 x x - y + 2 + 2 y x - y + 2 - 4 x - y + 2 = 3 x 2 - 3 x y + 6 x + 2 x y - 2 y 2 + 4 y - 4 x + 4 y - 8 = 3 x 2 - x y + 2 x - 2 y 2 + 8 y - 8 ∴ 3 x + 2 y - 4 × x - y + 2 = 3 x 2 - x y + 2 x - 2 y 2 + 8 y - 8

Evaluate: x 2 - 5 x + 8 × x 2 + 2 x - 3

Given expression: x 2 - 5 x + 8 × x 2 + 2 x - 3 Using horizontal method, we have x 2 - 5 x + 8 × x 2 + 2 x - 3 = x 2 x 2 + 2 x - 3 - 5 x x 2 + 2 x - 3 + 8 x 2 + 2 x - 3 = x 4 + 2 x 3 - 3 x 2 - 5 x 3 - 10 x 2 + 15 x + 8 x 2 + 16 x - 24 = x 4 - 3 x 3 - 5 x 2 + 31 x - 24 ∴ x 2 - 5 x + 8 × x 2 + 2 x - 3 = x 4 - 3 x 3 - 5 x 2 + 31 x - 24

Evaluate: 2 x 2 + 3 x - 7 × 3 x 2 - 5 x + 4

Given expression: 2 x 2 + 3 x - 7 × 3 x 2 - 5 x + 4 Using horizontal method, we have 2 x 2 + 3 x - 7 × 3 x 2 - 5 x + 4 = 2 x 2 3 x 2 - 5 x + 4 + 3 x 3 x 2 - 5 x + 4 - 7 3 x 2 - 5 x + 4 = 6 x 4 - 10 x 3 + 8 x 2 + 9 x 3 - 15 x 2 + 12 x - 21 x 2 + 35 x - 28 = 6 x 4 - x 3 - 28 x 2 + 47 x - 28 ∴ 2 x 2 + 3 x - 7 × 3 x 2 - 5 x + 4 = 6 x 4 - x 3 - 28 x 2 + 47 x - 28

Evaluate: 9 x 2 - x + 15 × x 2 - x - 1

Given expression: 9 x 2 - x + 15 × x 2 - x - 1 Using horizontal method, we have 9 x 2 - x + 15 × x 2 - x - 1 = 9 x 2 x 2 - x - 1 - x x 2 - x - 1 + 15 x 2 - x - 1 = 9 x 4 - 9 x 3 - 9 x 2 - x 3 + x 2 + x + 15 x 2 - 15 x - 15 = 9 x 4 - 10 x 3 + 7 x 2 - 14 x - 15 ∴ 9 x 2 - x + 15 × x 2 - x - 1 = 9 x 4 - 10 x 3 + 7 x 2 - 14 x - 15

E M B I B E

Mathematics Class 8>Chapter 6 - Operations on Algebraic Expressions>EXERCISE

R S Aggarwal Solutions for Chapter: Operations on Algebraic Expressions, Exercise 2: EXERCISE

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Chapter: Operations on Algebraic Expressions, Exercise 2: EXERCISE

Attempt the practice questions on Chapter 6: Operations on Algebraic Expressions, Exercise 2: EXERCISE with hints and solutions to strengthen your understanding. Mathematics Class 8 solutions are prepared by Experienced Embibe Experts.