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Download 9.3 Find Special Products of Polynomials
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&IND 3PECIAL 0RODUCTS OF 0OLYNOMIALS 'OAL 9OUR .OTES + 5SE SPECIAL PRODUCT PATTERNS TO MULTIPLY POLYNOMIALS 315!2% /& ! ")./-)!, 0!44%2. !LGEBRA A B A Ê ÊÓ>LÊ B A B A Ê ÊÓ>LÊ B %XAMPLE X X Ê ÊnÝÊ X X Ê Ê£ÓÝÊ %XAMPLE 5SE THE SQUARE OF A BINOMIAL PATTERN &IND THE PRODUCT 3OLUTION 7HEN YOU USE SPECIAL PRODUCT PATTERNS REMEMBER THAT A AND B CAN BE NUMBERS VARIABLES OR VARIABLE EXPRESSIONS A X X Ê ÊÓ{Ý®Î®Ê X Ê ÊÓ{ÝÊ B X Y X Ê ÊÓÎÝ®xÞ®Ê Y X Ê ÊÎäÝÞÊ Y #HECKPOINT &IND THE PRODUCT X Ê Ê Ý ÓÊÊ£nÝÊÊn£ X Ê Ê {Ý ÓÊÊÓnÝÊÊ{ R S Ê Ê ÓxÀ ÓÊÊ£äÀÃÊÊÃ Ó #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY ,ESSON s !LGEBRA .OTETAKING 'UIDE 9OUR .OTES 35- !.$ $)&&%2%.#% 0!44%2. !LGEBRA A BA B Ê >Ê Ê LÊ %XAMPLE X X Ê Ý Ê Ê £ÈÊ %XAMPLE 5SE THE SUM AND DIFFERENCE PATTERN &IND THE PRODUCT 3OLUTION A N N Ê Ê Ê ÎÊ 3UM AND DIFFERENCE PATTERN Ê Ê Ê Ê 3IMPLIFY B X YX Y Ê {Ý®Ê Ê ÞÊ Ê £ÈÝÊ Ê ÞÊ %XAMPLE 3UM AND DIFFERENCE PATTERN 3IMPLIFY 5SE SPECIAL PRODUCTS AND MENTAL MATH 5SE SPECIAL PRODUCTS TO FIND THE PRODUCT + 3OLUTION .OTICE THAT IS LESS THAN Ê ÓäÊ WHILE IS MORE THAN Ê ÓäÊ + Ê ÓäÊ Ê ÓäÊ ,ESSON s !LGEBRA .OTETAKING 'UIDE 7RITE AS PRODUCT Ê ÓäÓÊÊÎÓÊ 3UM AND DIFFERENCE PATTERN Ê {ääÊÊÊ %VALUATE POWERS Ê Î£Ê 3IMPLIFY #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY 9OUR .OTES #HECKPOINT #OMPLETE THE FOLLOWING EXERCISES &IND THE PRODUCT Z Z Ê Ê â ÓÊÊÎÈ &IND THE PRODUCT X X Ê Ê £ÈÝ ÓÊÊ &IND THE PRODUCT X YX Y Ê Ê Ý ÓÊÊÓxÞ Ó $ESCRIBE HOW YOU CAN USE SPECIAL PRODUCTS TO FIND Ê Ê 1ÃiÊÌ iÊõÕ>ÀiÊvÊ>ÊL>Ê«>ÌÌiÀÊÌÊv`ÊÌ iÊ «À`ÕVÌÊ{äÊÊ£®Ó° #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY ,ESSON s !LGEBRA .OTETAKING 'UIDE 9OUR .OTES %XAMPLE 3OLVE A MULTISTEP PROBLEM %YE #OLOR !N OFFSPRINGgS EYE COLOR IS DETERMINED BY A COMBINATION OF TWO GENES ONE INHERITED FROM EACH PARENT %ACH PARENT HAS TWO COLOR GENES AND THE OFFSPRING HAS AN EQUAL CHANCE OF INHERITING EITHER ONE 4HE GENE " IS FOR BROWN EYES AND THE GENE B IS FOR BLUE EYES !NY GENE COMBINATION WITH A " RESULTS IN BROWN EYES 3UPPOSE EACH PARENT HAS THE SAME GENE COMBINATION "B 4HE 0UNNETT SQUARE SHOWS THE POSSIBLE GENE COMBINATIONS OF THE OFFSPRING AND THE RESULTING EYE COLOR s 7HAT PERCENT OF THE POSSIBLE GENE COMBINATIONS OF THE OFFSPRING RESULT IN BLUE EYES s 3HOW HOW YOU COULD USE A POLYNOMIAL TO MODEL THE POSSIBLE GENE COMBINATIONS OF THE OFFSPRING 3OLUTION 3TEP .OTICE THAT THE 0UNNETT SQUARE SHOWS THAT Ê £Ê OUT OF OR Ê Óx¯Ê OF THE POSSIBLE GENE COMBINATIONS RESULT IN BLUE EYES 3TEP -ODEL THE GENE FROM EACH PARENT WITH Ê ä°xÊÊä°xLÊ 4HE POSSIBLE GENE OF THE OFFSPRING CAN BE MODELED BY Ê ä°xÊÊä°xL®ÓÊ .OTICE THAT THIS PRODUCT ALSO REPRESENTS THE AREA OF THE 0UNNETT SQUARE Ê ä°xÊÊä°xL®ÓÊ Ê ä°x®ÓÊÊÓä°x®ä°xL®ÊÊä°xL®ÓÊ Ê ä°Óx ÓÊÊä°xLÊÊä°ÓxL ÓÊ 4HE COEFFICIENTS SHOW THAT Ê Óx¯Ê OF THE POSSIBLE GENE COMBINATIONS WILL RESULT IN BLUE EYES (OMEWORK #HECKPOINT #OMPLETE THE FOLLOWING EXERCISE %YE #OLOR ,OOK BACK AT %XAMPLE 7HAT PERCENT OF THE POSSIBLE GENE COMBINATIONS OF THE OFFSPRING RESULT IN BROWN EYES Çx¯ ,ESSON s !LGEBRA .OTETAKING 'UIDE #OPYRIGHT Ú -C$OUGAL ,ITTELL(OUGHTON -IFFLIN #OMPANY