Expand and simplify (x − 4)(2x + 3y)^2

following BIDMAS we start with the second expression by squaring it, i.e. (x-4)(2x + 3y)(2x + 3y). It is important we do it in the right order, otherwise we could get a wrong answer. We use the FOIL (First Outside Inside Last) method to expand(2x + 3y)(2x + 3y)=(4x^2+6xy+6xy+9y^2) which simplifies to (4x^2+12xy+9y^2)
we then take that expression and multiply by (x-4) taking care of the signs and powers, and extending our FOIL method to ensure each term in the first bracket is multiplied by each term in the second.(x-4)(4x^2+12xy+9y^2)= (4x^3 + 12x^2y + 9xy^2 - 16x^2 - 48xy - 36y^2)