Factorize the following expression:(2x+3y)^2-(x-4y)^2?

To factorize the expression (2x+3y)^2-(x-4y)^2, we can use the difference of squares formula:

(a^2 - b^2) = (a + b)(a - b)

Let's rewrite the expression using this formula:

(2x+3y)^2 - (x-4y)^2
= [(2x+3y) + (x-4y)][(2x+3y) - (x-4y)]
= (2x + 3y + x - 4y)(2x + 3y - x + 4y)
= (3x - y)(x + 7y)

Therefore, the factorized form of the expression (2x+3y)^2-(x-4y)^2 is (3x - y)(x + 7y).

(2x 3y)^2-(x-4y)^2

=(2x 3y+x-4y)(2x 3y-x+4y)

=(3x - y)(x + 7y)