Questions: (a-2b)(2a+b)

(a-2b)(2a+b)
Transcript text: $(a-2 b)(2 a+b)$
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Solution

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Solution Steps

Step 1: Define the Expression

We start with the expression (a2b)(2a+b)(a - 2b)(2a + b).

Step 2: Apply the Distributive Property

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)

Step 3: Combine Like Terms

After performing the multiplications, we have: 2a2+ab4ab2b2 2a^2 + ab - 4ab - 2b^2 Now, we combine the like terms abab and 4ab-4ab: 2a23ab2b2 2a^2 - 3ab - 2b^2

Thus, the expanded form of the expression (a2b)(2a+b)(a - 2b)(2a + b) is: 2a23ab2b2 2a^2 - 3ab - 2b^2

Final Answer

2a23ab2b2\boxed{2a^2 - 3ab - 2b^2}

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