This post looks at more advanced R1 multiplications using expressions. The examples show that R1 multiplication of expressions is commutative.
Multiplication of Expressions that Contain Terms
A term can be multiplied with an Opposite Value. Multiplication is commutative. For example: x*2v = 2v*x.
Firstly, look at the equation (x + 1v )*(x + 3^) and (x + 3^)*(x + 1v ) with x = 2^.
| If x = | 2^ |
| x + 1v = | 1^ |
| x + 3^ = | 5^ |
| (x + 1v) (x + 3^) = 1^*5^ = | 5^ |
| (x + 1v) (x + 3^) = x2 + x*3^ + 1v*x + 1v*3^ = | 4^ + 6^ + 2v + 3v = 5^ |
| (x + 3^) (x + 1v) = 5^*1^ = | 5^ Note that it is commutative |
Secondly, look at the equation with x = 2v.
| If x = | 2v |
| x + 1v = | 3v |
| x + 3^ = | 1^ |
| (x + 1v) (x + 3^) = 3v *1^ = | 3v |
| (x + 1v) (x + 3^) = x2 + x*3^ + 1v*x + 1v*3^ = | 4^ + 6v + 2^+ 3v = 3v |
| (x + 3^) (x + 1v) = 1^*3v = | 3v Note that it is commutative |
Other examples:
- (x + 3^)(x + 3v) = x2 + 3vx + 3^x + 9v = x2 + 9v
- (x + 3^)(x + 3^) = x2 + 3^x + 3^x + 9^ = x2 + 6^x + 9^
- (x + 3v)(x + 3v) = x2 + 3vx + 3vx + 9^ = x2 + 6vx + 9^
Conclusion
Finally, try these examples of advanced R1 multiplication with our online calculator.
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