Question

Factorise completely x^8-y^8​

Answer 1

ANSWER.

• Factorised form » (x⁴ + y⁴)(x² + y²)(x + y)(x - y)

SOLUTION.

Given –

= x⁸ - y⁸

This can be written as,

= (x⁴)² - (y⁴)²

Using identity a² - b² = (a + b)(a - b), we get,

= (x⁴ + y⁴)(x⁴ - y⁴)

= (x⁴ + y⁴)[(x²)² - (y²)²]

Again, using same identity, we get,

= (x⁴ + y⁴)(x² + y²)(x² - y²)

= (x⁴ + y⁴)(x² + y²)(x + y)(x - y)

Which is our required answer.

MORE IDENTITIES TO KNOW.

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