University:
California State University, Northridge
Course:
MATH 150A | Calculus I
Academic year:

2024
Views:

67

Pages:

2
Author:

Fachtitelb00

I. MONOMIAL ARITHMETIC Addition and Subtraction When adding or subtracting monomials we combine the numerical parts only if letter parts are the same. i.e. The only algebraic terms which can be combined are like terms. Example: Find the sum of 14xyz , 2xy , -3xyz , 4xz , and -5xz 14xyz + 2xy + (-3xyz) + 4xz + (-5xz) = 14xyz - 3xyz + 4xz - 5xz + 2xy = 11xyz - xz + 2xy Example: Subtract -5ab from the sum of 7a2b , 2ab , 3ab2 and -6ab To avoid errors put -5ab in parenthesis and then subtract as follows : 7a2b + 2ab + 3ab2 + (-6ab) - (-5ab) = 7a2b + 2ab + 3ab2 - 6ab + 5ab = 2ab - 6ab + 5ab + 7a2b + 3ab2 = -4ab + 5ab + 7a2b + 3ab2 = ab + 7a2b + 3ab2 Multiplication and Division The product of monomials will give us another monomial . We multiply the number parts . The letter parts are multiplied by adding the exponents . Example: Find the product of 7a2b , abc , 3ab2 and -6a3bd 7a2b × abc × 3ab2 × (-6a3bd) = 7 × 3 × (-6) × a2 × a × a × a3 × b × b × b2 × b × c × d = 7 × 3 × (-6) × a2 + 1 +1 +3 × b1 + 1 + 2 + 1 × c × d = -126a7b5cd When dividing algebraic expressions we can cancel factors as follows : Example: Divide 27a2b3c by 9ab2c3 We must be careful with exponents : Example: 1.True or false (-5)0 = -50 2.True or false 5ab3 = 5(ab)3 Both equations are false . Solution to # 1 : (-5)0 = 1 while -50 = -1 therefore (-5)0 is not equal to -50 . When -5 is not enclosed in parenthesis the 0 exponent operates only on the 5 and not the negative sign in front of the 5 . Solution to # 2 : The solution is similar to the solution for #1 . With 5ab3 the 3 exponent operates only on the b . With 5(ab)3 the 3 exponent operates on everything within the parenthesis .