1 and the final value is 10. B.3 INTRODUCTORY ALGEBRA B.3 INTRODUCTORY ALGEBRA B.3.1 Review of the Laws of Signs If we multiply a + factor by another + factor, the product will have a + sign. If we divide a + factor by another + factor, the quotient will have a + sign. If we multiply a - factor by a + factor, the product will have a - sign (i.e., will be negative). Likewise, if we multiply a + factor by a - factor, the product will have a - sign. If we divide a + factor by a - factor, the quotient will have a - sign. Likewise, if we divide a - factor by a + factor, the quotient will have a - sign. If we divide a - factor by a - factor, the quotient will have a + sign. other words, +; and - -/- - = +. B.3.2 Conventions with Factors and Parentheses Two symbols placed together imply multiplication. Each symbol or symbol grouping is called a factor. Examples: xy means X multiplied by y. x(y + 1) means X multiplied by the quantity (y + 1). abc means a multiplied by b that is then multiplied by C. The use of parentheses is vital in algebra. If a parentheses pair has a sign in front of it, that sign is operative on each term inside the parentheses. If the sign is just a +, then consider that each term inside the parentheses is multiplied by +1. Here we just have a flow through. Example. Simplify 3X + (7X + Y - 10) = + + Y - 10 = 10X + Y - 10. Suppose there is a minus sign in front of the parentheses. Assume it is a -1. For the terms inside the parentheses, we change each sign and add. Consider nearly the same example: Simplify 3X - (7X + Y - 10) = 3X - 7X - Y + 10 = -4X - Y + 10. One more example: Simplify 4.5K - (-27.3 + 2.5K) = 4.5K + 27.3 - 2.5K = 2K + 27.3. We carry this one step further by placing a factor1 in front of the parentheses. Example. Simplify: 4X - (X2 + 2XY + 10) 5X2Y - 10XY2 - 50Y - 36. Another example: Simplify: 4Q 21(5Q2/3 = 4Q - 105Q2/3 + 03Q/6+84=4Q-35Q2+212/2+84=292/2-352284. - = - An algebraic expression may have parentheses inside brackets. The rule is to clear the "outside" first. In other word