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1) 3a^2 + 12ab + 12b^2
2) a^3 - 3b +a^2b - 3a
3) a^5 + 3a^3 - 8a^2 - 24
1) 3a^2 + 12ab + 12b^2
2) a^3 - 3b +a^2b - 3a
3) a^5 + 3a^3 - 8a^2 - 24
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Answers & Comments
1) 3a^2 + 12ab + 12b^2 = 3*(a² + 4ab + 4b²) = 3*(a + 2b)²
2) a^3 - 3b +a^2b - 3a = (a³ + a²b) - (3b + 3a) = a²(a + b) - 3(a + b) = (a + b)(a² - 3)
3) a^5 + 3a^3 - 8a^2 - 24 = a³(a² + 3) - (a² + 3) = (a² + 3)(a³ - 1) =
= (a² + 3)(a - 1)(a² + a + 1)