Ex. 12. Find the English equivalents for the following Russian words and word combinations.

1. утверждение; 2. иметь дело; 3. рассматривать; на языке; 4. вычислять; 5. подобно, таким же образом; 6. алгебраические выражения; 7. полином; 8. для удобства; 9. член; 10. трехчлен; 11. возведение в степень; 12. тогда утверждение справедливо; 13. представлять

 

a. then the statement is true; b. trinomial; c. raising to a power; d. deal with; e. for convenience; f. term; g. compute; h. likewise; i. in terms of; j. algebraic expressions; k. statement; l. represent; m. polynomial

 

Ex. 13. Give the proper English equivalents for the Russian expressions.

computed, instead of, simpler, ordinary letters, replace, hold, generalization, relations, concerning, multinomials

1. Algebra is обобщение of arithmetic. 2. In order to state the general rule we write symbols, обычные буквы, instead of particular numbers. 3. These signs have been introduced to denote отношения between numbers. 4. Algebra is the system of rules относительно the operations with numbers. 5. Particular numbers may замещать the symbols a and b. 6. All the laws of arithmetic верны for operations with letters. 7. We write symbols вместо particular numbers. 8. The square of the sum of any two numbers c and d can be вычислен by the rule (c + d)² = c² + 2c•d². 9. Algebraic expressions may be given a более простая form by combining similar terms. 10. Algebraic expressions consisting of more than one term are called полиномами.

 

Ex. 14. Mark the following as True or False.

1. Algebra is a generalization of geometry. 2. In order to state the general rule, we write numbers instead of particular letters. 3. Algebra is the system of rules concerning the operations with numbers. 4. Since the letters used represent numbers, all the laws of arithmetic fail to hold in operations with letters. 5. The operations of addition, subtraction, multiplication, division, raising to a power and extracting roots are called algebraic expressions. 6. An expression of two terms is a trinomial. 7. As in arithmetic, the equality sign means “not equal to”.8. In finding the product of multinomials we make use of commutative law. 9. These rules cannot be easily stated as formulas in terms of letters, like the rule given above for squaring the product of two numbers. 10. The outstanding characteristic of algebra is the use of numbers to represent letters.