Question

factorize;- (a) a6+ 4a3- 1

Answer 1

1. heya mate your answer is in the attachment☺️❤️

Answer 2

The factorization of a⁶ + 4a³ - 1 is equal to (a³ + 2 - √5)(a³ + 2 + √5).

Given:

The given expression is a⁶ + 4a³ - 1.

To Find:

The factorization of a⁶ + 4a³ - 1.

Solution:

The given expression is a⁶ + 4a³ - 1.

→ Adding and Subtracting '4' in the given expression in order to make a whole square:

      = a⁶ + 4a³ - 1 + 4 - 4

      = a⁶ + 4a³ + 4 - 4 - 1

→ Now using the formula (a² + b² + 2ab) = (a + b)², we get:

      = (a³)² + 2×(2)a³ + (2)²  - 5

      = (a³ + 2)² - 5

→ Now using the formula (a² - b²) = (a - b)(a + b) to factorize:

      = (a³ + 2)² - (√5)²

      = (a³ + 2 - √5)(a³ + 2 + √5)

Hence the factorization of a⁶ + 4a³ - 1 is equal to (a³ + 2 - √5)(a³ + 2 + √5).

#SPJ2