Question

how to solve 23³ - 17³ using identities​

Answer 1

Given

23³ - 17³

Solve it by using identity

Solution

★ Applying identity :

a³ - b³ = (a - b)(a² + ab + b²)

➥ 23³ - 17³

➥ (23 - 17)[(23)² + 23 × 17 + (17)²]

➥ 6 [529 + 391 + 289]

➥ 6 × 1209

➥ 7254

Some identities

• (a+b)² = a² + b² +2ab
• (a-b)² = a² + b² - 2ab
• (a+b)³ = a³ + b³ + 3ab(a+b)
• (a-b)³ = a³ -b³ - 3ab(a-b)
• a² - b² = (a+b)(a-b)
• a³ + b³ = (a+b)(a² - ab +b²)
• a³ - b³ = (a-b)(a² + ab + b²)

Answer 2

Given

23³ - 17³

Applying identity to solve this question

Solution

➞ 23³ - 17³

**Using identity :: (a - b)(a² + ab + b²)**

➞ (23 - 17) [ (23)² + 23*17 + (17)² ]

➞ (6) [ 569 + 391 + 289 ]

➞ 6 × 1209

➞ 7254

Identities

• (a+ b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• a² - b² = (a + b)(a -b)