Questions: Multiply the binomials using the FOIL method. Combine like terms. (6 x+2)(3 x+1)

Multiply the binomials using the FOIL method. Combine like terms. (6 x+2)(3 x+1)
Transcript text: Multiply the binomials using the FOIL method. Combine like terms. \[ (6 x+2)(3 x+1) \]
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Solution

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Solution Steps

To multiply the binomials \((6x + 2)(3x + 1)\) using the FOIL method, we need to apply the distributive property in a specific order: First, Outer, Inner, Last. This means we multiply the first terms of each binomial, then the outer terms, followed by the inner terms, and finally the last terms. After performing these multiplications, we combine any like terms to simplify the expression.

Step 1: Apply the FOIL Method

To multiply the binomials \((6x + 2)(3x + 1)\), we use the FOIL method, which stands for First, Outer, Inner, Last. This involves multiplying the terms in the following order:

  • First: Multiply the first terms of each binomial: \(6x \cdot 3x = 18x^2\).
  • Outer: Multiply the outer terms: \(6x \cdot 1 = 6x\).
  • Inner: Multiply the inner terms: \(2 \cdot 3x = 6x\).
  • Last: Multiply the last terms: \(2 \cdot 1 = 2\).
Step 2: Combine Like Terms

After applying the FOIL method, we combine the like terms:

  • The terms \(6x\) and \(6x\) are like terms and can be combined: \(6x + 6x = 12x\).
Step 3: Write the Final Expression

The expression after combining like terms is: \[ 18x^2 + 12x + 2 \]

Final Answer

\(\boxed{18x^2 + 12x + 2}\)

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