Technical Mathematics, Sixth Edition

Chapter 2. Introduction to Algebra

OBJECTIVES When you have completed this chapter, you should be able to Define common algebraic terms: variable, expression, term, polynomial, and so forth. Identify and define an equation. Separate a term into variables and constants. Simplify an expression by removing symbols of grouping. Add and subtract polynomials. Use the laws of exponents for multiplication, division, and raising to apower. Multiply monomials, binomials, and multinomials. Raise a multinomial to a power. Divide a polynomial by a monomial or by a polynomial.

In Chapter 1 we showed how to raise a number to a power. For example, 3² or 3 raised to the power 2, means

3² = (3)(3)

In a similar way, x², or x raised to the power 2, means

x² = (x)(x)

where x can stand for any number, not just 3. Going further, we can represent the exponent by a symbol, say n. Thus

While 3² was an arithmetic expression, xⁿ is an algebraic expression. We can think of algebra as a generalization of arithmetic. Some knowledge of algebra is essential in technical work. Suppose, for example, you see in a handbook that the power P delivered to a resistor, Fig. 2-1, is equal to VI, the voltage times the current. Then in another place you find that P is equal to V²/R, the square of the voltage divided by the resistance. In a third book you see that the power is equal to I²R, the square of the current times the resistance! ...