Question

answer the following questions using what youve learned from this lesson. write your responses in the space provided.

for questions 1 - 2, use the distributive property to find the product of the binomials.

1. ((x - 4)(2x + 5)) 2. ((4x - 2)(x - 3))

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

1. ((2x + 3)(x + 1)) 4. ((x - 5)(3x + 2))

Explanation:

Question 1: \((x - 4)(2x + 5)\)

Step 1: Apply distributive property (FOIL)

Multiply each term in the first binomial by each term in the second binomial:
\(x \cdot 2x + x \cdot 5 - 4 \cdot 2x - 4 \cdot 5\)

Step 2: Simplify each term

\(2x^2 + 5x - 8x - 20\)

Step 3: Combine like terms

\(2x^2 - 3x - 20\)

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

Step 1: Apply distributive property (FOIL)

\(4x \cdot x + 4x \cdot (-3) - 2 \cdot x - 2 \cdot (-3)\)

Step 2: Simplify each term

\(4x^2 - 12x - 2x + 6\)

Step 3: Combine like terms

\(4x^2 - 14x + 6\)

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

Step 1: First terms

\(2x \cdot x = 2x^2\)

Step 2: Outer terms

\(2x \cdot 1 = 2x\)

Step 3: Inner terms

\(3 \cdot x = 3x\)

Step 4: Last terms

\(3 \cdot 1 = 3\)

Step 5: Combine terms and simplify

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

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

Answer:

s:

1. \(2x^2 - 3x - 20\)
2. \(4x^2 - 14x + 6\)
3. \(2x^2 + 5x + 3\)
4. \(3x^2 - 13x - 10\)