Verified answer

a² - b² = (a - b)(a + b)

a³ - + b³ = (a - + b)(a² + - ab + b²)

(a +- b)² = a² +- 2ab + b²

(a^n)^m = a^nm

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2a^1/2(a^1/2 - 4) + 8a^1/2 = 2a^1/2*a^1/2 - 8a^1/2 + 8^1/2 = 2a

(3b^2/3 - c^3/2)(3b^2/3 + c^3/2) = (3b^2/3)^2 - (c^3/2)^2 = 9b^4/3 - c^3

(a^1/3 + b^1/3)² = (a^1/3)² + 2a^1/3b^1/3 + (b^1/3)² = a^2/3 + 2a^1/3b^1/3 + b^2/3

(b^0.4 + 3)² - 6b^0.4 = (b^0.4)² + 2*3*b^0.4 + 9 - 6b^0.4 = b^0.8 + 9

(c^1/3 - 1)(c^2/3 + c^1/3 + 1) = (c^1/3)³ - 1 = c - 1

(a^1/3 + a^1/2)(a^2/3 - a^5/6 + a) = (a^1/3 + a^1/2)( (a^1/3)² - a^1/2a^1/3 + (a^1/2)²) = (a^1/3)³ + (a^1/2)³ = a + a^3/2

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