Question

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Explanation:

Identify the expression to multiply

We are given the expression \((2x + 2)(3x + 1)\) to multiply. We will apply the FOIL Method to expand these binomials.

Apply the FOIL method

Using the FOIL Method, we multiply the terms in order: First, Outer, Inner, Last.

• First: Multiply the first terms of each binomial:

$$ (2x)(3x) = 6x^2 $$

• Outer: Multiply the outer terms:

$$ (2x)(1) = 2x $$

• Inner: Multiply the inner terms:

$$ (2)(3x) = 6x $$

• Last: Multiply the last terms of each binomial:

$$ (2)(1) = 2 $$

Combine the terms

Now, we write the sum of all the multiplied terms:

$$ 6x^2 + 2x + 6x + 2 $$

Simplify by combining like terms

Using the Polynomial Simplification process, we group and combine the like terms \(2x\) and \(6x\):

$$ 2x + 6x = (2 + 6)x = 8x $$

Substituting this back gives the final simplified polynomial:

$$ 6x^2 + 8x + 2 $$

Answer:

Multiply the binomials using the FOIL method. Combine like terms.
\((2x + 2)(3x + 1) =\) <blank>\(6x^2 + 8x + 2\)</blank>