Evaluate: (A + 1)(A2 - a + 1) and (A - 1)(A2 + a + 1)

Evaluate: (a + 1)(a² - a + 1) and (a - 1)(a² + a + 1)

Sum

(a + 1)(a² - a + 1) and (a - 1)(a² + a + 1)

= a (a² - a + 1) + 1 (a² - a + 1)

= a³ - a² + a + a² - a + 1

= a³ + 1

(a - 1)(a² + a + 1)

= a(a² + a + 1) - 1(a² + a + 1)

= a³ + a² + a - a² - a - 1

= a³ - 1

Now, (a + 1)(a² - a + 1) + (a - 1)(a² + a + 1)

= a³ + 1 + a³ - 1

= 2a³

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Chapter 11: Fundamental Concepts (Including Fundamental Operations) - Exercise 11 (C)

Chapter 11 Fundamental Concepts (Including Fundamental Operations)
Exercise 11 (C) | Q 5.4