(a+2b)(4a+b)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (a + 2b)(4a + b)

This article will guide you through the process of expanding the algebraic expression (a + 2b)(4a + b). We will use the FOIL method, a helpful mnemonic for multiplying binomials.

FOIL stands for First, Outer, Inner, Last, which refers to the order in which we multiply the terms:

1. First: Multiply the first terms of each binomial.
2. Outer: Multiply the outer terms of the binomials.
3. Inner: Multiply the inner terms of the binomials.
4. Last: Multiply the last terms of each binomial.

Applying FOIL to (a + 2b)(4a + b):

• First: (a)(4a) = 4a²
• Outer: (a)(b) = ab
• Inner: (2b)(4a) = 8ab
• Last: (2b)(b) = 2b²

Combining the terms:

Now we have: 4a² + ab + 8ab + 2b²

Finally, we combine the like terms:

4a² + 9ab + 2b²

Therefore, the expanded form of (a + 2b)(4a + b) is 4a² + 9ab + 2b².