Addition and multiplication - the basic mathematical operations standing in the same row with subtraction, division, exponentiation, and others. Combining these operations among themselves, it is possible to receive new, more difficult operations.
Instruction
1. To increase the sum by number, multiply everyone composed with this number, put the received numbers among themselves. Example. (a+b+c) *p=a*p+b*p+c*p. The return operation - removal of the general multiplier for a bracket: a*p+b*p+c*p=p(a+b+c).
2. For multiplication of two brackets comprising the sums of some variables there is a certain scheme. It is necessary to increase at first composed the first bracket on each of composed the second bracket, to put the received results, then to do the same operation with the second and subsequent composed the first bracket. It was necessary to put the received numbers among themselves. Example. (a+b) * (c+d) =a*c+a*d+b*c+b*d. Remember that are multiplied as well signs before numbers. The work of identical signs gives plus, different signs - minus. For example, (a-b) (c+d) =a*c+a*d-b*c-b*d; (a-b) (CD) =a*c-a*d-b*c+b*d. The return operation - decomposition of the sum on multipliers.
3. To multiply three brackets which are the sums of some variables it is necessary to multiply at first any two brackets, then to increase the received result by the third bracket. Multiplication of four and bigger numbers of brackets happens similarly. Group brackets so that it was more convenient and simpler to consider.
4. A special case of the work of the sums - construction of the sum in degree. For example, (a+b) ^2, (CD) ^3, (p-k) ^6. It is possible to present exponentiation in the form of the work of several identical brackets and to multiply them by the rules stated above. And it is possible to use formulas of abridged multiplication which are always useful for remembering.