a^2 + 4a + 4 = (a+2)^2, so it is a square
I don't understand why is this square, please help
Returning to your question of yesterday:
http://www.jiskha.com/display.cgi?id=1229063130
You know that the rectangle area is (a+2)^2 and that the width is (a+2). You were told that in the statement of the problem. Since the height of a rectangle is (area)/(width), the height (the other dimension) must also be a+2.
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To understand why the expression a^2 + 4a + 4 is a square, we need to examine its components and notice a pattern.
Let's break down the expression a^2 + 4a + 4:
- The first term, a^2, is the square of the variable 'a'.
- The second term, 4a, is twice the product of 'a' and 2 (2a).
- The third term, 4, is the square of 2.
Now, let's compare this expression to (a + 2)^2:
- The expression (a + 2)^2 means squaring the variable 'a' plus twice the product of 'a' and 2 (2a) plus the square of 2.
- Comparing it to a^2 + 4a + 4, we can see that both expressions have the same terms.
Therefore, a^2 + 4a + 4 is equivalent to (a + 2)^2, which is the square of the binomial (a + 2).