To expand this, we put it in the form (a + b)2 and expand it using the third rule above, which says:

(a + b)2 = a2 + 2ab + b2

I put

a = x + 2

b = 3y

This gives me:

(x + 2 + 3y)2

[This is the (a + b)2 step.]

= ([x + 2] + 3y)2

= [x + 2]2 + 2[x + 2](3y) + (3y)2

[Here I apply: (a + b)2 = a2 + 2ab + b2]

= [x2 + 4x + 4] + (2x + 4)(3y) + 9y2

[In this row I just expand out the brackets.]

= x2 + 4x + 4 + 6xy + 12y + 9y2

[This is a "tidy up" step.]

I could have chosen the following and obtained the same answer:

a = x

b = 2 + 3y

Try it!

Get the Daily Math Tweet!
IntMath on Twitter