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

Answer 1

To multiply the two binomials \( (4x + 1)(5x - 2) \), we can use the distributive property (also known as the FOIL method for binomials).

1. First: Multiply the first terms: \[ 4x \cdot 5x = 20x^2 \]

2. Outer: Multiply the outer terms: \[ 4x \cdot (-2) = -8x \]

3. Inner: Multiply the inner terms: \[ 1 \cdot 5x = 5x \]

4. Last: Multiply the last terms: \[ 1 \cdot (-2) = -2 \]

Now, combine all these results together: \[ 20x^2 - 8x + 5x - 2 \]

Combine like terms (\(-8x\) and \(5x\)): \[ 20x^2 - 3x - 2 \]

So, the product of \( (4x + 1)(5x - 2) \) is: \[ \boxed{20x^2 - 3x - 2} \]