We start with the expression (a−2b)(2a+b)(a - 2b)(2a + b)(a−2b)(2a+b).
Using the distributive property, we multiply each term in the first binomial by each term in the second binomial: (a)(2a)+(a)(b)+(−2b)(2a)+(−2b)(b) (a)(2a) + (a)(b) + (-2b)(2a) + (-2b)(b) (a)(2a)+(a)(b)+(−2b)(2a)+(−2b)(b)
After performing the multiplications, we have: 2a2+ab−4ab−2b2 2a^2 + ab - 4ab - 2b^2 2a2+ab−4ab−2b2 Now, we combine the like terms ababab and −4ab-4ab−4ab: 2a2−3ab−2b2 2a^2 - 3ab - 2b^2 2a2−3ab−2b2
Thus, the expanded form of the expression (a−2b)(2a+b)(a - 2b)(2a + b)(a−2b)(2a+b) is: 2a2−3ab−2b2 2a^2 - 3ab - 2b^2 2a2−3ab−2b2
2a2−3ab−2b2\boxed{2a^2 - 3ab - 2b^2}2a2−3ab−2b2
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