Question

for questions 3 - 5, use the foil method to find the product of the binomials.

1. $(2x + 3)(x + 1)$
2. $(x - 5)(3x + 2)$
3. $(x^2 + 2)(5x + 1)$

Explanation:

Question 3: \((2x + 3)(x + 1)\)

Step 1: Apply FOIL (First, Outer, Inner, Last)

First: \(2x \times x = 2x^2\)
Outer: \(2x \times 1 = 2x\)
Inner: \(3 \times x = 3x\)
Last: \(3 \times 1 = 3\)

Step 2: Combine like terms

\(2x^2 + 2x + 3x + 3 = 2x^2 + 5x + 3\)

Step 1: Apply FOIL (First, Outer, Inner, Last)

First: \(x \times 3x = 3x^2\)
Outer: \(x \times 2 = 2x\)
Inner: \(-5 \times 3x = -15x\)
Last: \(-5 \times 2 = -10\)

Step 2: Combine like terms

\(3x^2 + 2x - 15x - 10 = 3x^2 - 13x - 10\)

Step 1: Apply FOIL (First, Outer, Inner, Last)

First: \(x^2 \times 5x = 5x^3\)
Outer: \(x^2 \times 1 = x^2\)
Inner: \(2 \times 5x = 10x\)
Last: \(2 \times 1 = 2\)

Step 2: Combine like terms (no like terms to combine here, so just arrange)

\(5x^3 + x^2 + 10x + 2\)

Answer:

\(2x^2 + 5x + 3\)

Question 4: \((x - 5)(3x + 2)\)