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This is the "grid" or "boxes" structure which gives the multiplication method its name. Faced with a slightly larger multiplication, such as 34 × 13, pupils may initially be encouraged to also break this into tens. So, expanding 34 as 10 + 10 + 10 + 4 and 13 as 10 + 3, the product 34 × 13 might be represented:
A multiplication algorithm is an ... A person doing long multiplication on paper will write down all the products and ... (2 + 10)*47 but don't add up the partial ...
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. It is frequently used to transform the antiderivative of a product of functions into an ...
The product of a sequence, vector multiplication, complex numbers, and matrices are all examples where this can be seen. These more advanced constructs tend to affect the basic properties in their own ways, such as becoming noncommutative in matrices and some forms of vector multiplication or changing the sign of complex numbers.
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A telescoping product is a finite product (or the partial product of an infinite product) that can be canceled by the method of quotients to be eventually only a finite number of factors. [ 7 ] [ 8 ] It is the finite products in which consecutive terms cancel denominator with numerator, leaving only the initial and final terms.