-ULTIPLY 0OLYNOMIALS
'OAL
9OUR .OTES
+ -ULTIPLY POLYNOMIALS
%XAMPLE -ULTIPLY A MONOMIAL AND A POLYNOMIAL
&IND THE PRODUCT X X X X 3OLUTION
X X X X X Ê ÓÝ ÎÊ X Ê Ý ÓÊ X Ê ÇÝ Ê X Ê ÎÊ Ê ÈÝ ÈÊ Ê ÎÝ xÊ Ê Ó£Ý {Ê Ê ™Ý ÎÊ
%XAMPLE -ULTIPLY POLYNOMIALS VERTICALLY AND HORIZONTALLY
&IND THE PRODUCT
A A A A 2EMEMBER THAT THE
TERMS OF A z
ARE A AND 4HEY ARE NOT A
AND 3OLUTION
A 6ERTICAL FORMAT
A z
B B B B A A 7RITE THE PRODUCT
IN VERTICAL FORMAT
Ê ÓÊ A Ê £ÓÊ A Ê ÈÊ ÊÊA
-ULTIPLY BY Ê xÊ -ULTIPLY BY Ê Ó>Ê Ê Ó>ÎÊÊÊ Ê £ÇÊ >ÓÊÊÊ Ó{Ê >ÊÊÊ £xÊ
!DD PRODUCTS
Ê xÊ A Ê ÎäÊ A Ê £xÊ
B (ORIZONTAL FORMAT
B B B Ê ÎL ÓÊ B Ê ÓL Ê B Ê xÊ B Ê £xLÎÊÊ£nLÓÊÊ£äLÓÊÊ£ÓLÊÊÓxLÊÊÎäÊ
Ê £xLÎÊÊÓnLÓÊÊÎÇLÊÊÎäÊ
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9OUR .OTES
#HECKPOINT &IND THE PRODUCT
X X zX zX z
Ê
Ê ÓÝ xÊÊ£äÝ {ÊÊÈÝ ÎÊÊ£{Ý Ó
A zA zA z
Ê
Ê Ó>ÎÊÊ£Î>ÓÊÊÇ>ÊÊ£Ó
%XAMPLE -ULTIPLY BINOMIALS USING THE &/), PATTERN
&IND THE PRODUCT C C 3OLUTION
C C CÊ VÊ CÊ ™Ê Ê VÊ Ê ™Ê Ê ÓV ÓÊÊ­£nV ®ÊÊÇV ÊÊ­ÈήÊ
Ê ÓV ÓÊÊ££V ÊÊÈÎÊ
#HECKPOINT #OMPLETE THE FOLLOWING EXERCISE
&IND THE PRODUCT M M Ê
Ê x“ÓÊÊ££“ÊÊ£Ó
,ESSON s !LGEBRA .OTETAKING 'UIDE
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9OUR .OTES
%XAMPLE -ULTIPLY PONYNOMIALS TO FIND AN AREA
!REA 4HE DIMENSIONS OF A RECTANGLE ARE X AND
X 7RITE AN EXPRESSION THAT REPRESENTS THE AREA
OF THE RECTANGLE
3OLUTION
!REA LENGTH + WIDTH
&ORMULA FOR AREA
OF A RECTANGLE
Ê ÝÊÊ{Ê Ê ÝÊÊxÊ 3UBSTITUTE FOR
LENGTH AND WIDTH
Ê Ý ÓÊÊxÝÊÊ{ÝÊÊÓäÊ
-ULTIPLY BINOMIALS
Ê Ý ÓÊʙÝÊÊÓäÊ
#OMBINE LIKE
TERMS
#(%#+ 5SE A GRAPHING CALCULATOR
TO CHECK YOUR ANSWER 'RAPH
Y Ê ­ÝÊÊ{®­ÝÊÊx®Ê AND
Y Ê ­Ý ÓÊʙÝÊÊÓä®Ê IN THE
SAME VIEWING WINDOW 4HE GRAPHS
Ê Vœˆ˜Vˆ`iÊ SO THE PRODUCT OF
X AND X IS Ê Ý ÓÊʙÝÊÊÓäÊ #HECKPOINT #OMPLETE THE FOLLOWING EXERCISE
4HE DIMENSIONS OF A RECTANGLE ARE X AND
X 7RITE AN EXPRESSION THAT REPRESENTS THE
AREA OF THE RECTANGLE
Ê
Ê Ý ÓÊÊ£{ÝÊÊÎÎ
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,ESSON s !LGEBRA .OTETAKING 'UIDE
9OUR .OTES
%XAMPLE 3OLVE A MULTISTEP PROBLEM
7ALKWAY 9OU ARE MAKING A
A WALKWAY AROUND PART OF
YOUR SWIMMING POOL 4HE
DIMENSIONS OF THE SWIMMING
POOL AND WALKWAY ARE SHOWN
IN THE DIAGRAM
s 7RITE A POLYNOMIAL THAT REPRESENTS THE AREA OF THE
SWIMMING POOL
s 7HAT IS THE AREA OF THE SWIMMING POOL IF THE WALKWAY
IS FEET WIDE
3OLUTION
3TEP 7RITE A POLYNOMIAL USING THE FORMULA FOR THE AREA
OF A RECTANGLE 4HE LENGTH IS Ê ÓxÊÊÝÊ 4HE WIDTH
IS Ê £nÊÊÝÊ !REA Ê i˜}Ì…Ê + Ê Üˆ`̅Ê
Ê ­ÓxÊÊÝ®­£nÊÊÝ®Ê
Ê {xäÊÊÓxÝÊÊ£nÝÊÊÝ ÓÊ
Ê {xäÊÊ{ÎÝÊÊÝ ÓÊ
3TEP 3UBSTITUTE Ê ÓÊ FOR X AND EVALUATE
!REA Ê {xäÊÊ{έӮÊÊ­Ó®ÓÊ Ê ÎÈnÊ
4HE AREA OF THE SWIMMING POOL IS Ê ÎÈnÊõÕ>ÀiÊviiÌÊ #HECKPOINT #OMPLETE THE FOLLOWING EXERCISE
(OMEWORK
3WIMMING 0OOL 9OUR NEIGHBOR
HAS A WALKWAY AROUND HIS
ENTIRE POOL AS SHOWN IN
THE DIAGRAM 4HE WIDTH OF
THE WALKWAY IS THE SAME
ON EVERY SIDE 7RITE A
POLYNOMIAL THAT REPRESENTS
THE AREA OF THE POOL 7HAT IS THE AREA
OF THE POOL IF THE WALKWAY IS FEET WIDE
ÈÈäÊÊ£ä{ÝÊÊ{Ý ÓÆÊÎn{ÊõÕ>ÀiÊviiÌ
,ESSON s !LGEBRA .OTETAKING 'UIDE
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