Expand and simplify the following:

$\left(a+9\right)\left(b-6\right)$(a+9)(b−6)

Expand the following using binomial expansion:

$\left(x+5\right)\left(x+7\right)$(x+5)(x+7)

$\left(4r+7\right)\left(7s+2\right)$(4r+7)(7s+2)

$\left(2n+5\right)\left(5n+2\right)-4$(2n+5)(5n+2)−4

Expand and simplify second-degree polynomial expressions involving one variable that consist of the product of two binomials [e.g., (2x + 3)(x + 4)] or the square of a binomial [e.g., (x + 3)^2], using a variety of tools and strategies