Question

\[\left[ (a+b)+3 \right]^{2}\]

Answer 1

Multiply it out:
\[((a+b) + 3)((a+b) + 3) = (a+b+3)(a+b+3) =\]
Multiply each term in the first set of parentheses with each term in the second set. Collect like terms.

Answer 2

awesome

Answer 3

a(a+b+3)+b(a+b+3)+3(a+b+3)?

Answer 4

Yes, now expand that out and collect like terms.

Answer 5

thyaks

Answer 6

if you dont want to open up those round parentheses straight away ;,\[\left[ (a+b)+3 \right]^{2}\]\[=\left[ (a+b)+3 \right]\left[ (a+b)+3 \right]\]\[= (a+b)\left[ (a+b)+3 \right]+3 \left[ (a+b)+3 \right]\]\[= (a+b)^2+3(a+b)+ 3(a+b)+3^2\]\[= (a+b)^2+6(a+b)+3^2 \]

Answer 7

Going even further in that direction, let c = (a+b), then
\[(c+3)(c+3) = c^2 + 3c + 3c + 9 = c^2 + 6c + 9 = (a+b)^2 + 6(a+b) + 9\]

Answer 8

And then if you want to destroy the nice look, you can expand those to
\[(a^2 + 2ab + b^2) + 6(a+b) + 9 = a^2 + b^2 + 2ab + 6a + 6b + 9\]

Answer 9

you guys rock