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

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

Solution

Solution Steps

Step 1: Define the Expression

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

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: \[ (a)(2a) + (a)(b) + (-2b)(2a) + (-2b)(b) \]

Step 3: Combine Like Terms

After performing the multiplications, we have: \[ 2a^2 + ab - 4ab - 2b^2 \] Now, we combine the like terms $ab$ and $-4ab$: \[ 2a^2 - 3ab - 2b^2 \]

Thus, the expanded form of the expression $(a - 2b)(2a + b)$ is: \[ 2a^2 - 3ab - 2b^2 \]

Final Answer

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

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