We are asked to expand the expression $(x+4y)(x-3y)$.

1. Problem Description

We are asked to expand the expression $(x+4y)(x-3y)$.

2. Solution Steps

To expand the expression $(x+4y)(x-3y)$, we use the distributive property (also known as the FOIL method):

$(x+4y)(x-3y) = x(x) + x(-3y) + 4y(x) + 4y(-3y)$

$= x^2 - 3xy + 4xy - 12y^2$

$= x^2 + (4xy - 3xy) - 12y^2$

$= x^2 + xy - 12y^2$

3. Final Answer

$x^2 + xy - 12y^2$