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