Expand and simplify (x − 4)(2x + 3y)^2
Rewrite (x − 4)(2x + 3y)2 as (x - 4)(2x + 3y)(2x + 3y)
Multiply out the first two brackets to give -(2x2 + 3xy - 8x2 - 12y)(2x + 3y)
Multiply out the remaining brackets4x3 + 6x2y - 16x2 - 24xy + 24xy + 6x2y + 9xy2 - 24xy - 36y2
Simply what's left...4x2 + 12x2y + 9xy2 – 16x2 – 48xy – 36y2
Therefore...(x − 4)(2x + 3y)2 = 4x2 + 12x2y + 9xy2 – 16x2 – 48xy – 36y2
