Now say we also have a rectangle whose length is also a, but whose width is given by a variable b. The area of this rectangle is a x b = ab.
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If you attach one each of these ab rectangles to the right and bottom of the first square, you get a shape that is almost a square. Like so:
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The area of this shape is the sum of the other shapes: (a x a) + (a x b) + (a x b) = a^2 + 2ab, which are the first two terms of the expansion I mentioned in the beginning. Now, what about the third term? Since the last piece to be filled is another square, and its sides are equal to b:
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Our third term is b^2, and the square is complete.
How does this relate to a quadratic equation, you ask?
A quadratic equation can be simplified into two forms that makes assumptions about quadratic graphs a lot clearer. It reduces the number of x variables from two to one, and can be used to find the vertices, axis of symmetry, and maximum/minimum points of a quadratic parabola.
These two forms are:
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