Simplification Copyrighted by T Darrel Westbrook Simplification In
Simplification Copyrighted © by T. Darrel Westbrook
Simplification In this lesson you will learn What to Simplify? 26 August 2010 Alg 2_Simplification. ppt Copyrighted © T. Darrel Westbrook 2
Simplification Denominator Can’t Have Combine Like Terms All Parenthesis Removed Rational Numbers Complex Numbers Radical Numbers Negative Numbers 26 August 2010 What to Simplify? All Fractions Are Reduced Alg 2_Simplification. ppt Copyrighted © T. Darrel Westbrook No Negative Exponents Index of All Radicals as Small As Possible 3
Simplification Combine Like Terms 25 and Why Are is x. How What and about Simplify x– 13 is two a xlike term? different andterms? y? terms? 2+ 2 4 x 2 +– 72 x 3 x g(x) 3 x= 2 x +– 2 x 5 –+– 3 x 75 =–=f(x) x 3 x –=52 y+ 3 x 7 26 August 2010 Alg 2_Simplification. ppt Copyrighted © T. Darrel Westbrook g(x) 5 x 4 x 22 –=+x 3 x 2 x– –+ 5 x = 2= f(x) +y 7 4
Simplification All Parenthesis Removed g(x) = f(x) h(x) (2 x x 2 =+=–– 3 x – 3) 5(2 x (4 x –=(4 x f(x) –– 27) 3)– 7) 26 August 2010 2= g(x) f(x) h(x) 2 x ==––=– 4 x 3– 10 x 4 x +f(x) +3 x + 15 7+ 7 Alg 2_Simplification. ppt Copyrighted © T. Darrel Westbrook 5
Simplification No Negative Exponents 1 – 3 x +2 x– 4 = k(x) x – 3 26 August 2010 1 11 x 41 1 + x 4 + x = 4 3 x+=3 3 = 3 x 2 x x 16 x 3 Alg 2_Simplification. ppt Copyrighted © T. Darrel Westbrook 6
Simplification Index of All Radicals as Small As Possible 3 44/6/28 2/½ 2 = =3 a 2 =3 =2 3 22 a 68 4 12 2 a 26 August 2010 Alg 2_Simplification. ppt Copyrighted © T. Darrel Westbrook 7
Simplification All Fractions Are Reduced 7 x x 3 1 6/ g(x) k(x) =+– /2 x += 4 x– 4 6 46 26 August 2010 14 x 3 x 1 17 x + k(x) == x – 4= 12 12 Alg 2_Simplification. ppt Copyrighted © T. Darrel Westbrook g(x) 8
Simplification Denominator Can’t Have Rational Numbers Complex Numbers Radical Numbers Negative Numbers No Fractions In Denominator Numbers of the Form a + bi Numbers of the Form No Negative Numbers In Denominator x 5/ 6 3 – 2 + 5 i 3 2 x – 9 3 – 2 1 a How to eliminate complex and radicals from the denominator will be discussed in a later lesson. 26 August 2010 Alg 2_Simplification. ppt Copyrighted © T. Darrel Westbrook 9
Simplification Expressions, equalities, or inequalities all follow the same simplification process. Simplification and Order of Operations adds deterministic structure to mathematics (means there is no ambiguity). This means that if you and another student of mathematics work the same problems containing grouping symbols and operators, you both will get the same answer (assuming, of course, you made no simplification, arithmetic, or Order of Operations errors). 26 August 2010 Alg 2_Simplification. ppt Copyrighted © T. Darrel Westbrook 10
Simplification END OF LINE 26 August 2010 Alg 2_Simplification. ppt Copyrighted © T. Darrel Westbrook 11
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