(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: $$\boxed{{\displaystyle 20x^2-3x-2}}$$