Morphing
When solving an equation, we often do some operation that involves rearranging the symbols with minor alterations. Symbol motion covers this kind of operation. Other times, we need to replace a few symbols with something else entirely. This happens when we are simplifying or reducing part of the equation. Some simple examples are if we take an expression 4x - x and replace it with 3x, or if we take 
and simplify it to x. An alteration like this, applied to the image of an expression, is called a morph. A morph is when we take a group of symbols in the image of an equation, and replace it with a smaller or simpler group of symbols that is mathematically equal. The concept is not a big deal; that's exactly what you are doing when you simplify or reduce something, and you do that all the time. So why do we have a whole chapter about it? The difference is that while substitution is a mathematical action, morphing is a visual action. Morphs are often used when doing some kind of substitution, in a broad sense of the word. There are some patterns we can use that make the task easier. This chapter explains them and how to use them. We start with a kind of morph called fusion, and then introduce more general morphs.
This bonus material is available in the full version.
This bonus material is available in the full version.
This bonus material is available in the full version.