Question

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))
2. ((x^2 + 2)(5x + 1))

Explanation:

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

Step 1: Distribute \(x\) and \(-4\)

\(x(2x + 5) - 4(2x + 5)\)

Step 2: Multiply each term

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

Step 3: Combine like terms

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

Step 1: Distribute \(4x\) and \(-2\)

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

Step 2: Multiply each term

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

Step 3: Combine like terms

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

Step 1: Multiply First terms

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

Step 2: Multiply Outer terms

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

Step 3: Multiply Inner terms

\(3 \cdot x = 3x\)

Step 4: Multiply Last terms

\(3 \cdot 1 = 3\)

Step 5: Combine like terms

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

Answer:

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

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