Answer:
(3x−y)(x+7y)
Step-by-step explanation:
Factor (2x+3y)^2−(x−4y)^2
3x^2+20xy−7y^2
=(3x−y)(x+7y)
(3x - y)(x + 7y)
Given
(2x + 3y)² - (x - 4y)² ← is a difference of squares and factors in general as
a² - b² = (a + b)(a - b)
Here a = 2x + 3y and b = x - 4y , then
(2x + 3y + x - 4y)(2x + 3y - (x - 4y))
= (3x - y)(2x + 3y - x + 4y) = (3x - y)(x + 7y)
Thus
(2x + 3y)² - (x - 4y)² = (3x - y)(x + 7y) ← in factored form
