The problem requires us to multiply the two binomials $(5x + 6)$ and $(8x + 1)$ and simplify the resulting expression.

1. Problem Description

The problem requires us to multiply the two binomials $(5x + 6)$ and $(8x + 1)$ and simplify the resulting expression.

2. Solution Steps

We need to multiply the two binomials $(5x + 6)(8x + 1)$ using the distributive property (also known as the FOIL method).

$(5x + 6)(8x + 1) = 5x(8x + 1) + 6(8x + 1)$

Now, distribute $5x$ across $(8x + 1)$:

$5x(8x + 1) = 5x(8x) + 5x(1) = 40x^2 + 5x$

Next, distribute $6$ across $(8x + 1)$:

$6(8x + 1) = 6(8x) + 6(1) = 48x + 6$

Now, add the two results:

$(40x^2 + 5x) + (48x + 6) = 40x^2 + 5x + 48x + 6$

Combine like terms:

$40x^2 + (5x + 48x) + 6 = 40x^2 + 53x + 6$

3. Final Answer

$40x^2 + 53x + 6$