RATIONAL ALGEBRAIC EXPRESSIONS and Operations.pptx

operations on rational algebraic expressions

1. Operations of Rational Algebraic Expression

2. Multiplying Rational Algebraic Expressions The product of two rational expressions is the product of the numerators divided by the product of the denominators. In symbols,  

3. Multiplying Rational Algebraic Expressions Find the product of   Express the numerators and denominators into prime factors       Simplify rational expressions using laws of exponents

4. Dividing Rational Algebraic Expressions The quotient of two rational expressions is the product of the dividend and the reciprocal of the divisor.

5. Adding and Subtracting Dissimilar Rational Algebraic Expressions In adding or subtracting dissimilar rational expressions, change the rational algebraic expressions into similar rational algebraic expressions using the least common denominator or LCD and proceed as in adding similar fractions

6. Adding and Subtracting Dissimilar Rational Algebraic Expressions Find the sum of  

7. FACTORING DIFFERENCE OF TWO SQUARES

8. Factoring Difference of Two Squares The factored form of a polynomial that is a difference of two squares is the sum and difference of the square roots of the first and last terms.

9. Factoring Difference of Two Squares         (  

10. Factor         9  

11. Factor          

12. Factor          

13. Factor          

14. FACTORING Sum and DIFFERENCE OF TWO cubes

15. Factoring the Sum and Difference of Two Cubes The polynomial in the form  is called the  sum  of two cubes because two cubic terms are being added together. That is:   The polynomial in the form  is called the  difference  of two cubes because two cubic terms are being deducted together. That is:  

16. Factor         =      

17. Factor         =        

18. Factor         =        

19. Factor         =        

20. Factor         =        

21. Factor         =        

22. FACTORING Perfect square trinomial and general trinomial

23. Perfect Square Trinomials You can use the following relationships to factor perfect squares:    

24. Factor            

25. Factor            

26. Factor            

27. Factor            

28. Factor            

29. General Trinomials To factor trinomials with 1 as the numerical coefficient of the leading term : a. Factor the leading term of the trinomial and write these factors as the leading terms of the factors; b. List down all the factors of the last term; c. Identify which factor pair sums up to the middle term; then d. Write each factor in the pairs as the last term of the binomial factors.

30. Factor     Factors Product Sum 7 3 21 10 1 21 21 22 -7 -3 21 -10 -1 -21 21 -22 Factors =        

31. Factor     Factors Product Sum 2 3 6 5 6 1 6 7 -2 -3 6 -5 -6 -1 6 -7 Factors =        

32. Factor     Factors Product Sum -3 7 -21 4 -7 3 -21 -4 -21 1 -21 -20 -1 21 -21 20 Factors =        

33. Factor the expression using the Greatest Common Monomial Factor   Factor the Difference of Two Squares 3. 4.   Factor the Sum and Difference of Two Cubes 5. 6.   Factor the Perfect Square Trinomials 7. 8 .   Factor the General Trinomials that has a leading coefficient 1 9. 10 .  

34. Rational Algebraic Expressions

35. Group Activity 1 1. The ratio of a number x and four added to two. 2. The product of the square root of three and the number y . 3. The square of a added to twice the a . 4. The sum of b and two less than the square of b . 5. The product of p and q divided by three. 6. One third of the square of c . 7. Ten times a number y increased by six. 8. The cube of a number z decreased by nine. 9. The cube root of nine less than a number w . 10. A number h raised to the fourth power.                    

36. Rational Algebraic Expressions All polynomials are expressions but not all expressions are polynomials. A rational algebraic expression is a ratio of two polynomials provided that the denominator is not equal to zero. In symbols: , where and are polynomials and  

37. Group Activity 2 RATIONAL ALGEBRAIC EXPRESSIONS NOT RATIONAL ALGEBRAIC EXPRESSIONS IDENTIFY THE FOLLOWING EXPRESSIONS                

38. Recall Laws of Exponents I. Product of Powers   II. Power of a Power   IV. Power of a Quotient   III. Power of a Product    

39. Group Activity 3 REWRITE EACH EXPRESSIONS WITH POSITIVE EXPONENTS 1.   2.   3.   =   =   =  

40. Simplifying Rational Algebraic Expressions

41. Simplify:         GCF = 4

42. Simplify:         GCF = 3

43. Simplify:        

44. Simplify:    

45. Simplify:         1.   2.