Question

multiply the binomials using the foil method. combine like terms.

\\((8x + 5)(2x + 1)\\)

Explanation:

Identify the given expression

We are given two binomials to multiply:

$$ (8x + 5)(2x + 1) $$

Apply the FOIL method

To multiply these binomials, we use the FOIL Method to find the four individual products:

• First terms: \(8x \cdot 2x = 16x^2\)
• Outer terms: \(8x \cdot 1 = 8x\)
• Inner terms: \(5 \cdot 2x = 10x\)
• Last terms: \(5 \cdot 1 = 5\)

Write the expanded expression

Using Polynomial Multiplication, we sum the four products:

$$ 16x^2 + 8x + 10x + 5 $$

Combine like terms

Using Polynomial Simplification, we group and add the linear terms:

$$ 8x + 10x = (8 + 10)x = 18x $$

This yields the final simplified trinomial:

$$ 16x^2 + 18x + 5 $$

Answer:

Multiply the binomials using the FOIL method. Combine like terms.

\((8x + 5)(2x + 1) =\) <blank>\(16x^2 + 18x + 5\)</blank>