Question

Factorise the given expression a square minus 4b square minus a cube minus 8 b cube plus (A + 2B whole square

Answer 1

Answer:

Step-by-step explanation

Answer 2

a²  - 4b²  - a³  - 8b³  + (a + 2b)² = (a + 2b)(2a - a²  - 4b² + 6ab)

Step-by-step explanation:

a²  - 4b²  - a³  - 8b³  + (a + 2b)²

= a² - (2b)²  - ( a³  + (2b)³) + (a + 2b)²

= (a + 2b)(a - 2b)  -  ((a + 2b)³  - 3(a)2b(a + 2b))  + (a + 2b)(a + 2b)

= (a + 2b)(a - 2b + a + 2b)  - (a + 2b) ( (a+2b)² - 6ab)

= (a + 2b)(2a)  - (a + 2b) ( (a+2b)² - 6ab)

= (a + 2b)(2a)  - (a + 2b) ( a² + 4b² - 6ab)

= (a + 2b)(2a - a²  - 4b² + 6ab)

a²  - 4b²  - a³  - 8b³  + (a + 2b)² = (a + 2b)(2a - a²  - 4b² + 6ab)

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