Chapter 3: Algebraic Expressions Lesson Index & Summary
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- Hubert Bryant
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1 Chpter 3: Algebric Epressios Lesso Ide & Summry Sectio : Moomils Ide Bse Scree 6 Coefficiet Scree 4 Costt Scree 2 Degree Scree 7 Epded Form Scree 6 Epoet Scree 6 Epoetil Form Scree 6 Epoetil Nottio Scree 6, 7 Moomil Scree 2 Stdrd Form Screes 4, 6 Vrible Scree 2 Defiitios: (Scree 2) A vrible is letter or symbol used to represet qutity tht is ukow or c chge. The letters d y re the symbols most commoly used s vribles but y letter c be used. Vribles re lso sometimes referred to s "ukows." A costt is qutity tht does ot chge i vlue. A moomil is costt, vrible, or the product of costts d vribles. A moomil ever ivolves dditio, subtrctio, rdicls of vribles, or vribles i deomitor. The degree of moomil with oly oe vrible is simply the degree of tht vrible. (Scree 7) The degree of is sice The degree of costt is 0. =. (Scree 7) Pge of 7
2 Chpter 3: Algebric Epressios Lesso Ide & Summry Sectio 2: Bsic Rules for Epoets Ide Epoet, defiitio Scree 2 Epoet, rules/properties Scree 2, 3, 7 Order of Opertios, ow icludig epoets Scree Defiitio of Epoets: Rules of Epoets: Rule : Rule 2: of these = (Scree 2) =, for y rel umber. (Scree 2) = m m +, for y rel umber d y itegers m d. (Scree 2) Rule 3 ( ) y = y, for y rel umbers d y d y positive iteger. (Scree 3) Rule 4: ( m) Rule 5: y m =, for y rel umber d y itegers m d. (Scree 3) = y, for y d y, y 0, d y iteger. (Scree 7) The order of opertios is s follows: (Scree ) 2. Simplify withi pretheses. 3. Simplify y epoets. 4. Perform multiplictio d divisio from left to right. 5. Perform dditio d subtrctio from left to right. Some fid it helpful to keep i mid tht egtives re equivlet to multiplictio by : A = A. (Scree 3) ( ) A egtive umber rised to eve epoet is positive, but egtive umber rised to odd epoet is egtive. (Scree 3) The egtive sig is ot prt of the bse uless it is icluded i pretheses. (Scree 3) Pge 2 of 7
3 Chpter 3: Algebric Epressios Lesso Ide & Summry Sectio 3: Additiol Rules for Epoets Ide Elevtor Rule Scree Epoet, rules/properties Scree 5 Negtive epoet Scree 4 More Rules of Epoets: m Rule 6 (Ccelltio): m =, for y rel umber, 0, d y itegers m d. (Scree 2) 0 Rule 7: = for y rel umber 0. (Scree 3) Rule (Defiitio of Negtive Epoet): =, for y rel umber, 0, d for y iteger. (Scree 4) (Scree 5) Properties of Epoets = 2 m m+ = 3 ( ) b = b m 4 ( ) 5 6 m = b 7 0 m = = = = b m Remember tht the elevtor rule oly works whe the umertor d the deomitor re both completely fctored s products; if there is y dditio or subtrctio i the frctio, do NOT use this techique. (Scree ) Pge 3 of 7
4 Chpter 3: Algebric Epressios Lesso Ide & Summry Sectio 4: From Words to Algebric Epressios Ide Algebric equtios Scree 5 Algebric iequlities Scree 5 Reltiol symbols Scree 5 Commo word epressios tht idicte lgebric reltioships: is equl to = is ot equl to is less th < is less th or equl to is greter th > is greter th or equl to (Scree 5) Commo word phrses d their lgebric equivlets: (Screes 9-0) plus dded to icresed by more th + the sum of d the totl of d d together times the product of d multiplied by multiplied by s mius subtrcted from decresed by less th fewer th the differece of d divided by oe-eighth of eighth prt of or or the quotiet of d the rtio of d Pge 4 of 7
5 Chpter 3: Algebric Epressios Lesso Ide & Summry is less th is smller th < is greter th > is more th equls is = is equl to is greter th or equl to } is less th or equl to } does ot equl is ot is ot equl to Pge 5 of 7
6 Chpter 3: Algebric Epressios Lesso Ide & Summry Sectio 5: Evlutig Epressios Ide Evlute Scree 2 Evlute mes to substitute the give umber for the vrible d the simplify the epressio. Emple A: Evlute the moomil 2 =, the ( ) 2 If whe = 5. (Scree 2) 3 = 3 5 = 3 25 = 75. Emple D: Evlute b + 7 whe = 4 d b = 3. (Scree 3) Replce with 4 d b with 3 : b + 7 = =. Whe you substitute egtive umber for vrible, use pretheses. (Scree 4) Pge 6 of 7
7 Chpter 3: Algebric Epressios Lesso Ide & Summry Sectio 6: Polyomils Ide Biomils Scree 4 Combiig like terms Scree 4 Degree of polyomil Scree 6 Like terms Scree 4 Moomil (revisited) Scree 2 Polyomil Scree 2 Term Scree 4 Triomils Scree 4 A polyomil is moomil or the sum or differece of y umber of moomils. (Scree 2) Like terms c be dded. This is clled combiig like terms. Whe you combie like terms, you dd the coefficiets of ech term d leve the vrible prts uchged. Thus, y 9y + 7 y 4 = 2 y 9y 4. (Scree 4) We sw erlier tht the degree of moomil with oly oe vrible is simply the degree of tht vrible. Whe moomil hs more th oe vrible, the degree of the moomil is the sum of the epoets of ll the vribles of the moomil. (Scree 6) The degree of polyomil i stdrd form is the highest degree of y of its terms (ssumig its like terms hve ll bee combied). (Scree 6) A Word to the Wise Alwys combie like terms before decidig the degree of polyomil. (Scree 7) Pge 7 of 7
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