To expand this, we put it in the form `(a + b)^2` and expand it using the 3rd rule above, which says:
(a + b)2 = a2 + 2ab + b2
I put
`a = x + 2`
`b = 3y`
This gives me:
| (x + 2 + 3y)2 | |
| = ([x + 2] + 3y)2 | [This is the (a + b)2 step.] |
| = [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!