Question

Expand the following:

(x + 3y + 2) (x + 3y + 5)

Answer 1

Given: (x + 3y + 2)(x + 3y + 5)

Step-wise calculation:

Let z = x + 3y,

Then expression becomes:

(z + 2)(z + 5)

Expanding this:

z² + 5z + 2z + 10 = z² + 7z + 10

Substitute back z = x + 3y:

(x + 3y)² + 7(x + 3y) + 10

Expand (x + 3y)²:

x² + 2 × x × 3y + (3y)² = x² + 6xy + 9y²

Expand 7(x + 3y):

7x + 21y

So the full expanded form is x² + 6xy + 9y² + 7x + 21y + 10.