How do you simplify the following expression by adding (x+2y)(x+2y)

Question

I need help adding this expression I need an example to help.

Answer 1

The way it's written doesn't suggest addition.  I'll explain what I mean by giving you two answers :-).

 

If the equation truly is (x+2y)(x+2y), then you're multiplying those expressions together using FOIL, which stands for first, outer, inner, last.

First: x * x

Outer: x*2y

Inner: 2y * x

Last: 2y * 2y

So the expression is (x+2y)(x+2y) = x(x) +x(2y) +2y(x) + 2y(2y) = x² + 2xy +2yx +4y².  Because the two middle terms are really using the same variables (i.e. xy = yx), you can also combine those.  So the final answer is x²+4xy+4y².

 

NOW...if you're really ADDING the two expressions, I'd expect it to be written as such: (x+2y)+(x+2y).  IF that's the case, then you simply add those with similar variables (i.e. add the 'X's together and the 'Y's together).  If it helps, you can even drop the parenthesis if truly adding the expressions.  (Note: you cannot drop parenthesis when multiplying, dividing, or subtracting expression...only adding)

(x+2y)+(x+2y)

x+2y+x+2y

x+x+2y+2y     co-locate (or put together) similar variables

2x+4y             add them together

Answer 2

If what you mean was to add (x+2y)² to some other expression so the other expression simplifies, then you will need to provide that other expression to me so I can help you. Otherwise, here is how you simplify this expression.

First you want to use the distributive property, which says that a(b+c) = ab + ac.

   (x+2y)(x+2y)

= x(x+2y) + 2y(x+2y)

= x² + 2xy + 2xy + 4y²

The middle two terms can be added together to get 4xy, so that the expression becomes

x² + 4xy + 4y².

Another way to do this problem is to use the identity (a+b)² = a² + 2ab + b²

This gives (x+2y)² = x² + 2x(2y) + (2y)² = x² + 4xy + 4y²