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Chapter 6—Expressions and Equations 65 Removing Parentheses
When you see an algebraic expression in a science or business textbook, it is usually presented in its simplest form. Compare these two versions of the same expression: 2x + 3(x + 4) and 5x + 12 These expressions are the same. In other words, 2x + 3(x + 4) = 5x + 12. You can demonstrate this fact by substituting any value for the x's and solving the results. You can see that the expression, 5x + 2 is clearly simpler than the version that includes parentheses. The purpose of this lesson is to demonstrate how to simplify expressions by removing the parentheses. This procedure frequently uses the distributive property.
Removing Parentheses from Expressions of Form a(bx + c) Removing the parentheses from an expression of the form a(bx + c) is a matter of applying the basic distributive property: Examples A
The procedure for removing parentheses require a bit more care when negative values and subtraction are involved. Examples B
Examples & Exercises
Removing Sets of Parentheses that are Added/Subtracted Consider this messy looking expression: 2(x + 1) + 3(x + 6)
Result:
Examples C
Examples & Exercises
Removing Sets of Parentheses that are Multiplied Tutorial Example
(a + b)(c + d) = ac + ad + bc + bd –(a + b)(c + d) = –(ac + ad + bc + bd) = –ac – ad – bc – bd (a + b)(c + d + e) = ac + ad + ae + bc + bd + be (a + b)(c + d)(e + f) = (ac + ad + bc + bd)(e + f) = ace + acf + ade + + adf + bce + bcf + bde + bdf Tutorial Example Reduce this expression: (4x  2)(5x + 1) (4x  2)(5x + 1) = 20x2 + 1 10x 2
Examples C
(2 + 4)(3 + 5) (a + b)(c + d) a(c + d) + b(c + d) ac + ad + bc + bd
(2 + 4)(3 + 5) 2(3 + 5) + 4(3 + 5) 6 + 10 + 12 + 20 = 48 (2 + 4)(3 + 5) = 48 Note: This is the same as (2 + 4)(3 + 5) = (6)(8) = 48
(3 – 6)(2 + 5) 3(2 + 5) – 6(2 + 5) 6 + 15 – 12 – 30 = (3 – 6)(2 + 5) = – 21
(2x + 1)(4x – 1) 8x^{2} – 2x + 4x – 1 8x^{2} + 2x – 1
Result: (2x + 4)(5x  3) = 10x^{2} + 14x  12


David L. Heiserman, Editor  Copyright © SweetHaven
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Revised: June 06, 2015