;Algebra 1: FOIL Method ;copyright 2004 Inspired Idea All rights reserved

Transcription

1 ;Algera 1: FOIL Method ;opyright 004 Inspired Idea All rights reserved \presentation [foil.jpg][p]in algera a speial proess of multiplying two inomials together makes the aronym FOIL for First, Outer, Inner, Last. The FOIL Method makes it easier to omine like terms after multiplying two inomials.[foil] [p]knowledge of the FOIL Method will espeially e helpful for determining the fators[fatoring] of a trinomial[trinomial] and finding the points of a linear equation in latter lessons. \onept The FOIL Method[FOIL] is used in multiplying inomials[inomials] to make omining like terms[liketerms] easier. \or Using the FOIL Method[FOIL] helps to simplify the resulting polynomial[polynomial]. \or FOIL[foil] stands for the order of how the terms[term] of two inomials[inomial] are multiplied together: First, Outer, Inner, Last. \not The HILO Method is used when multiplying inomials. \not The FOIL Method[FOIL] is an unneessary proess sine simplifying any distriution[distriution] arrives at the same answer. \test Desrie the FOIL Method. \orret The FOIL Method is used in multiplying inomials to make omining like terms easier. \or Using the FOIL Method helps to simplify the resulting polynomial. \or FOIL stands for the order of how the terms of two inomials are multiplied together: First, Outer, Inner, Last.

2 \not The FOIL Method is when mathematiians plae aluminum foil on their heads to help their rains solve omple prolems. \not The FOIL Method is an unneessary proess sine simplifying any distriution arrives at the same answer. \infodistriution [p]the distriutive property states that for any natural numers a,, and, a ) a a or a a; and for any natural numers a,,, and d, a ) d) a ad d or a ad d. The order does not alter the solution. 3) ) or ; either way it equals 0. \infoliketerms [p]like terms have the same or no) variale to the same power. In the polynomial[polynomial] a a 3a, a and 3a are like terms. [p] When two inomials[inomial], eah with a like term, are multiplied together, the resulting polynomial[polynomial] will have two like terms whih an e omined to result in either a trinomial[trinomial] like a 5a or a inomial[inomial] like a. \info foil [p] One distriution[distriution] of a )a 3) is a a 3 a. The FOIL method assures that like terms[like terms] will e grouped together in the middle for easier simplifiation omining terms and/or reduing to lowest terms). This is ahieved y multiplying the []F[/]irst terms of eah inomial fator FIRST, then the two []O[/]utermost, the two []I[/]nnermost terms, and then the []L[/]ast remaining terms. By using the FOIL method First, Outer, Inner, Last) on our eample, we arrive at, so we an more easily omine the like a 3a a

3 terms and simplify it to a 5a. [p]when multiplying inomials, a sutration operand eomes a negative oeffiient. ) 3 5) 5 3) 3) 5) [n] ) y 7) y 7) y ) y 7) ) y y 7y y 4 y 13y 4 \infofatoring [p]the fators of 10 are and 5 sine X The fators of 3 are 1) and 3) sine. The proess of determining 1) 3) 3 the fators of a polynomial is alled fatoring. \infomonomial [p] A monomial one name in Latin) is a mathematial epression ontaining one term, suh as 10 or a or -3y or 3. \info inomial [p]a inomial two name in Latin) is a mathematial epression ontaining two terms, suh as 7-13 or a 5 or - 3y or 3y 7. [p]speial patterns result when a inomial is multiplied y itself. a a a a and ) ) a a a a ) )

4 [p]the middle terms add up to zero leaving the differene of two squares in the following situation: ) a ) a a a a a \infotrinomial [p] A trinomial three name in Latin) is a mathematial epression ontaining three terms, suh as 10 or 3a - 4 or 5-3y 1 or 3 3y 5. \infoterm [p] A term is a single mathematial epression, also alled a monomial[monomial], suh as 1 or 5. \infopolynomial [p] A polynomial many name in Latin) is a mathematial epression ontaining more than one term[term], suh as 1 or 3a - 4 7d or y 5y or 3 3. [p]polynomials are written in desending order from highest power to the lowest power; thus would e written as t) t) 40 5t t t [p]and t 13t 40 [p]polynomials usually egin with a positive term of highest power, even if that means fatoring out a negative one. 7 s s ) s) s 5 5 7s s s 1 ) s s 5) 5 s s \question->foil Aording to the FOIL Method, what are the Last terms in z - )z 7)? \orret -)7)

5 \or - and 7 \not -)z) \not 7)z) \not 7 and z \question->foil Aording to the FOIL Method, what are the Outer terms in 4) - 10)? \orret -10)) \or -10 and \not 4)-10) \not 4)) \not 4 and -10 \question-> Aording to the FOIL Method, what are the Inner terms in v - 3)v - )? \orret -3)v) \or -3 and v \not -3 and - \not -3)-) \not - and v \question->foil What are the results of using the FOIL method on a 1) a 3)? \orret a 4a 3 \or a 3a a 3 \or a 3a 1a 3 \not a 3 \not a a 3

6 \question->inomial Multiply the inomial[inomial] y y itself and simplify. \orret y 4y 4 \orret y ) y ) \not y ) y ) y y 4y 4 y 4 y \not 4 \fat->y3y3 y 3) y 3) \or ) \not ) \not ) \info y3y3 y y y 3 y y y 3 y y y 3 y y 3) y 3) y 3) y 3y 3y y y a 10a 5 a 5 a 5 a 10a 5 a 5 a 5a 5 a 5 a 5 \fat->a-5a-5 a 5) \or ) ) \not ) \not->inomial ) \info a-5a-5 ) a 5 a 5) a 5) a 5a 5a 5 a 10a 5 \question->-- What are the results of using the FOIL? method on ) ) \orret ) ) 1 4

7 \or ) 4 1 \not ) ) 1 4 \not ) 1 \info -- ) ) ) \question->-45 What are the results of using the FOIL method on ) ) 5 4? \orret ) ) \or ) ) \not->oef ) ) \not->-oef ) ) \infooef You ve multiplied the oeffiients of the middle terms. \info -oef You ve sutrated the oeffiients of the middle terms. \info -45 ) ) \fat->- ) ) 54 3 \or ) ) 54 \not ) ) \not->-oef ) ) \info - ) )

8 v) v 3v 40 5 v v) 40 3v v \fat->5v-v 5 v) \or ) \or ) ) ) 5 v v v 3v 40 1 v 3v 40) \not 5 v) v) v 3v 40 \not 5 v ) v) 40 13v v 5 v) v) 40 5v v v \info->5v-v 40 3v v ) 1 v 3v 40) v 3v 40 [p]polynomials usually egin with a positive term of highest power, even if that means fatoring out a negative one. \fat->a-a11 a ) a 11) a 11a 4 \or ) a a 11) a a 11a 4 \not->-oef ) a a 11) a 33a 4 \not ) a a 11) a 11a 33 \info->a-a11 a a 11 a a 11a 4 a ) ) 11a 4

9 \fat->1-r-r 1 r) r) 10 1r \or 1 r) r) r \not->-oef 1 r) r) \not 1 r) r) r r r 1r 10 1r 10 r 3r 10 1r 1 \info->1-r-r ) r) 1 r 10 1r r 10 1r r r 1r fat->y3y-3 y 3) y 3) y \or ) y 3 y 3) y 3y 3y y \not->-oef ) y 3 y 3) y y \not y 3) y 3) y \info->y3y-3 y 3 y 3 y 3y 3y y 0 y ) ) \fat->-44 4) 4) \or 4) 4) \not ) 4) \not->oef ) 4) 4 4) \dialog \hallenge->foil What is the result of the first step in the y y? FOIL proess of multiplying ) 10)

10 \response y \hallenge->foil What is the result of the seond step in the FOIL proess of multiplying y ) y 10)? \response 10y \hallenge->foil What is the result of the third step in the FOIL y y? proess of multiplying ) 10) \response -y \hallenge->foil What is the result of the last step in the FOIL y y? proess of multiplying ) 10) \response -0 \onlusion Corret, the FOIL proess of multiplying y ) y 10) results in y y 0. \dialog \hallenge->foil What is the result of the first step in the 7? FOIL proess of multiplying ) 3) \response \hallenge->foil What is the result of the seond step in the FOIL proess of multiplying - 7) 3)? \response 3 \hallenge->foil What is the result of the third step in the FOIL proess of multiplying - 7) 3)? \response -7 \hallenge->foil What is the result of the last step in the FOIL proess of multiplying - 7) 3)? \response -1 \onlusion Corret, the FOIL proess of multiplying - 7) 3) results in 4 1.

11 \dialog \hallenge->foil What is the result of the first step in the FOIL proess of multiplying 4 - w) w)? \response 4 \hallenge->foil What is the result of the seond step in the FOIL proess of multiplying 4 - w) w)? \response 4w \hallenge->foil What is the result of the third step in the FOIL proess of multiplying 4 - w) w)? \response -w \hallenge->foil What is the result of the last step in the FOIL proess of multiplying 4 - w) w)? \response w \onlusion Corret, the FOIL proess of multiplying 4 - w) w) results in 4 4w w w. \hallenge->polynomial How would you write 4 4w w w as a proper positive polynomial? \response 1) w w 4 \onlusion Though w w 4is orret, a negative one needs to e fatored out to avoid a negative variale at the eginning of a polynomial. \dialog \hallenge->foil What is the result of the first step in the FOIL proess of multiplying 4) )? \response \hallenge->foil What is the result of the seond step in the FOIL proess of multiplying 4) )?

12 \response \hallenge->foil What is the result of the third step in the FOIL proess of multiplying 4) )? \response 4 \hallenge->foil What is the result of the last step in the FOIL proess of multiplying 4) )? \response \onlusion Corret, the FOIL proess of multiplying 4) ) results in. \deoration \deoration \deoration foil.jpg foilfae.jpg foilre.jpg