3.4.Multiplicationa x b = ab = producta + a + a + a = 4aDivisiona ÷ b = a/b = quotientGROUPING—USE OF PARENTHESESOccasionally a combination of symbols must betreated as a single symbol. When this occurs, the groupis set apart by use of parentheses.In order to symbolize 5 times the sum of a + b, youshould write 5(a + b).The quotient of a + b divided by 2 is writtenREMOVAL OF COMMON FACTORSFROM AN EXPRESSION BY USE OFPARENTHESESIn the expression 2a + 2b + 2c: the common factormay be removed and the remainder combined in paren-theses: 2(a + b + c) or in the following: 4ab + 2ac + 6ax.All the terms contain the factor 2a. The expressionmay be changed to read 2a(2b + c + 3x).Since the parentheses indicate that each term withinis to be multiplied by the factor outside the parentheses,the parentheses may be removed by multiplying eachterm by the common factor.Expression: 2x(2y + 3Z + m)Multiply: 4 x y + 6 x z + 2 x mSUBSTITUTION OF NUMERICALVALUES FOR GROUPED SYMBOLSConsider the expression:5(a + b)2This means to first: add a and b. Second: multiply thesum by 5. Third: divide the product by 2.Assign numerical values to a and b.Let a = 4 and b = 2.Substitute:PERIMETERS ANDCIRCUMFERENCESPerimeter and circumference have the same mean-ing; that is, the distance around. Generally, circumfer-ence is applied to a circular object and perimeter to anobject bounded by straight lines.PERIMETER OF A POLYGONThe perimeter of a triangle, quadrilateral, or anyother polygon is actually the sum of the sides.Write an equation for the perimeter(P) of the quad-rilateral above.P = a + b + c + dIf this figure were a rectangle,the formula P= a + b + c + d would still apply, but sinceopposite sides are equal, we could substitute a for c andb ford and writeP = 2a + 2bIf the figure were a square, the formula wouldbecome:P = 4 aWe may, by the same reasoning, establish that theformula for the perimeter of any regular polygon of nsides having a sides is:P = n(s)AII-14

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