By Deborah Hughes-Hallett, William G. McCallum, Eric Connally
Shape is expounded to operate. An aircraft wing has the shape it does due to its lifting functionality. The pillars of the Parthenon and the girders of a skyscraper are formed to the aim of assisting their big constructions. equally, the shape of an algebraic expression or equation displays its functionality. Algebra: shape and serve as initial version introduces each one function--linear, energy, quadratic, exponential, polynomial--and provides a research of the fundamental type of expressions for that functionality. Readers are inspired to envision the fundamental kinds, see how they're built, and think about the position of every part. during the textual content, there are instruments sections positioned on the ends of chapters to assist readers gather the talents they should practice uncomplicated algebraic manipulations.
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Shape is expounded to operate. An plane wing has the shape it does due to its lifting functionality. The pillars of the Parthenon and the girders of a skyscraper are formed to the aim of aiding their substantial buildings. equally, the shape of an algebraic expression or equation displays its functionality.
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Additional info for Algebra: Form and Function
9. Add 2, double the result, then subtract 4. 27. t2 − 4t 28. t3 − 25t 29. t3 + 16t 30. t(t − 3) + 2(t − 3) 31. 4t1/2 − 4t 32. t2 (t + 5) + 9(t + 5) 33. t2 (t + 8) − 36(t + 8) 34. 4t2 (2t−3)−36(2t−3) 10. Divide by 5, subtract 2 from the result, then divide by 3. 11. Subtract 1, square the result, then add 1. 12. Divide by 2, subtract 3 from the result, then add the result to the result of first subtracting 3 from x and then dividing the result by 2. In Exercises 13–16, evaluate the expressions given that u = −2, v = 3, w = 2/3.
5. 3 EQUIVALENT EXPRESSIONS 6. 5r 7. 3(z + w) and 3z + 3w √ 9. a2 + b2 and a + b 11. (3 − 4t)/2 and 3 − 2t 2 2 2 8. (a − b)2 and a2 − b2 10. −a + 2 and −(a + 2) 12. bc − cd and c(b − d) 17 17. “Multiply by eighty percent” “Divide by eight-tenths” 18. The area of a triangle is often expressed as A = (1/2)bh. Is the expression bh/2 equivalent to the expression (1/2)bh? 19. Show that the following expressions have the same value at x = −8: 4 13. x + 4x , 5x , and 4x √ 14. (x + 2)2 , x2 + 4, and x4 + 16 In Exercises 15–17, (a) Write an algebraic expression representing each of the given operations on a number b.
2x2 + 3x3 = 5x5 8. 2AB 2 + 3A2 B = 5A3 B 3 −x + 5 and 9. 3h2 + 2h2 = 5h2 (2x)(2y) 5. (3x)(4y)(2x) 6. (x + 3)(4 + x) and and For Exercises 7–10, is the attempt to combine like terms correct? 24x2 y (x + 3)(x + 4) 10. 2 THE DISTRIBUTIVE LAW 33 14. (7x + 1) + (5 − 3x) + (2x − 4) In Exercises 11–18, write the expression in a simpler form, if possible. 15. 5x2 + 5x + 3x2 11. (2x + 1) + (5x + 8) 16. 3a + 5ab + 2b 12. (4 − 2x) + (5x − 9) 17. (2x)(3y) + 4x + 5y + (6x)(3y) 13. (x + 1) + (x + 2) + (x + 3) 18.
Algebra: Form and Function by Deborah Hughes-Hallett, William G. McCallum, Eric Connally