"Turn into a sum"
At some point in school, children are faced with the task of converting a product into a sum. "Transform" is actually a bad expression, because multiplying is not a mysterious trick, it is very easy.
Turn this product into a sum!
- This only works for products that contain at least one bracket in which a total is mentioned.
- First, identify the unknowns that are in the brackets.
- If the same unknowns are added within brackets, you can calculate this in advance: 4 * (x + x + y + y + y) = 4 * (2x + 3y)
- In the simplest example, a sum in brackets is multiplied by a number. In this case you have to multiply each addend in the brackets by this number and you can omit the brackets: 4 * (2x + 3y) = 8x + 12y
- If there is also an unknown outside the brackets, you must also multiply this by the summands in the brackets: 4x * (2x + 3y) = 8x² + 12xy
Solve equations in brackets - the math expert explains how it works
If there weren't any nasty brackets in the equations - who the rules ...
Multiply out for two sums in brackets
- If you have two sums that are multiplied together, you have to multiply each addend of one sum by each addend of the other sum: (4x + 2y) * (2x + 3y) = 8x² + 12xy + 6y² + 4xy
- You can now add the same unknowns or the same products from unknowns: 8x² + 12xy + 6y² + 4xy = 8x² + 16xy + 6y²
- If a third unknown is added, proceed in the same way: (4x + 2z) * (2x + 3y) = 8x² + 12xy + 4zx + 6zy (no further ones can be used here) summary take place.)
- If the sums get larger, nothing changes for your calculation, as you can see in this example: (4x + 3y + 2z) * (3x + 5y + 3z) = 12x² + 20xy + 12xz + 9yx + 15y² + 9yz + 6zx + 10zy + 6z²
- Since the exchange law applies within products and within sums, you can summarize here again: 12x² + 20xy + 12xz + 9yx + 15y² + 9yz + 6zx + 19zy + 6z² = 12x² + 15y² + 6z² + 29xy + 18xz + 28yz
So you see: "transform" is really not appropriate here; the multiplication is not magic, but a very simple calculation.
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