Simplify the following:

(2x+y+5)(2x+y-9)

(2x+y+5)(2x+y-9)

Let (2x+y)=z

Then the given expression = (z+5)(z-9)

We know that (x+a)(x-b) = x² + (a - b)x - ab

∴ (z+5)(z-9) = z² + (5-9)z - (5)(9)

= z² - 4z - 45

= (2x+y)² - 4(2x+y) - 45

= (2x)² + 2(2x)(y) + (y)² - 8x - 4y - 45

= 4x² + 4xy + y² - 8x - 4y - 45

= 4x² - 8x + y² - 4y + 4xy - 45