Simplify the following:

(x+2y+3)(x+2y+7)

(x+2y+3)(x+2y+7)

Let (x+2y)=z

Then the given expression = (z+3)(z+7)

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

∴ (z+3)(z+7) = z² + (3+7)z + (3)(7)

= z² + 10z + 21

= (x+2y)² + 10(x+2y) + 21

= x² + 2(x)(2y) + (2y)² + 10x + 20y + 21

= x² + 4xy + 4y² + 10x + 20y + 21

= x² + 10x + 4y² + 20y + 4xy + 21