(x+3)squared-(y+2)squared
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To simplify the expression (x+3)^2 - (y+2)^2, we can use the difference of squares formula. The difference of squares formula states that a^2 - b^2 can be factored as (a + b)(a - b).
In this case, our expression is (x+3)^2 - (y+2)^2. Using the difference of squares formula, we can rewrite it as [(x+3)+(y+2)][(x+3)-(y+2)].
Now, let's simplify each of the two factors separately.
The first factor, (x+3)+(y+2), can be further simplified by combining like terms. Adding x and y gives us x+y, then adding 3 and 2 gives us 5. So, (x+3)+(y+2) simplifies to x+y+5.
The second factor, (x+3)-(y+2), can also be simplified by combining like terms. Subtracting y from x gives us x-y, then subtracting 2 from 3 gives us 1. So, (x+3)-(y+2) simplifies to x-y+1.
Now, we can rewrite our expression as (x+y+5)(x-y+1). This is the simplified form of (x+3)^2 - (y+2)^2.