Question

Factorise (2x+3y)²-(x-4y)²​

Answer 1

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

Explanation:

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

Answer 2

(3x−y)(x+7y)

Explanation:

Factor (2x+3y)^2−(x−4y)^2

3x^2+20xy−7y^2

=(3x−y)(x+7y)