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Problem 13
If we want to multiply (x^3-3x^2+2x) with (x^3-2x^2+x), then we can set up a diagram shown below. The terms are along the outside. The stuff inside is the result of multiplying each pair of outer terms.
- Example: x^3 times x^3 = x^6 in the top left corner
- Another example: 2x times x = 2x^2 in the bottom right corner.
This is known as the box method to keep track of all the terms multiplied.
Once the table is filled out, we add up each term inside the boxes. Combine like terms if possible. Notice that I color-coded the like terms (eg: the x^3 terms are in green boxes).
The final answer is x^6 - 5x^5 + 9x^4 - 7x^3 + 2x^2
