Answer
$2xy(2x+3)(6x-5)$
Work Step by Step
Factoring an expression completely means writing it as a product of factors so that none of the factors can be further factored.
Factor each term of the given expression.
$=2^3\cdot 3x^3y+2^4x^2y-2\cdot 5\cdot 3xy$
Factor out the common factor.
$=2\cdot xy(2^2\cdot 3x^2+2^3x- 5\cdot 3)$
Simplify.
$=2xy(12x^2+8x- 15)$
Rewrite the middle term $8x$ as $18x-10x$.
$=2xy(12x^2+18x-10x- 15)$
Group the terms.
$=2xy[(12x^2+18x)+(-10x- 15)]$
Factor each group.
$=2xy[6x(2x+3)-5(2x+3)]$
Factor out $(2x+3)$.
$=2xy(2x+3)(6x-5)$
