alimov-7-algebra-gdz (Алгебра - 7 класс - Алимов), страница 12

1)4)10a − ba3−3a − ba3=10a − b − 3a + ba32 1 2+3 5;+ ==3a a3a3acd c + 5ad3);+ =15a 315a463. 1)464. 1) 5 −2)465. 1)3)4)466. 1)1002 3 5b 2 − 2b + 3+=;b b2b24a3b23y3+−5d6ab3126x y=+12a 3b3512 xy2=2a21 2 5−23−==b 5b5b5b4)3ad − bab−=4 12d12d; 2)c c 2 d 3 − cd + c 2+=d d2d2mm 2 mn − kn 2 + m 2−k + 2 =nnn24)9b 2c + 10a 2d72)3) d −232c + 4c 2 − 3+4− 2 =;ccc23c=2a9b 4−7c6a 3b=4a 4 − 21b3c18a 3b 428 x − 2 y + 5 xy12 x 2 y 3bbbbcd 2 + bd + cb+ 2 + 2 =c c d cdc2d 2x2x2 x + 3x5x=+=3 ⋅ (a − b ) a − b 3 ⋅ (a − b ) 3 ⋅ (a − b )2)7x5x7 x − 10 x3x−3 x−===2 ⋅ (x − 1) x − 1 2 ⋅ (x − 1) 2 ⋅ (x − 1) 2 ⋅ (1 − x )3)2a 25a 28a 2 + 15a 223a 2=+=3 ⋅ (a + 1) 4 ⋅ (a + 1) 12 ⋅ (a + 1) 12 ⋅ (a + 1)4)4y5x8 y − 25 x−=5 ⋅ ( y − 3) 2 ⋅ ( y − 3) 10 ⋅ ( y − 3)467.

1)2)3)3a2 + a+5a35a3b + 5a 23b + 5a 2=+== 2ab + b a ⋅ (a + 1) b ⋅ (a + 1) ab ⋅ (a + 1) a b + ab5b2a5b2a5b 2 − 2a 2−=−=ax + ay bx + by a ⋅ (x + y ) b ⋅ (x + y ) ab ⋅ (x + y )y+a+y −b=y+ay −bay + a 2 + by − b 2==+b ⋅ (b + a ) a ⋅ (b + a )ab ⋅ (b + a )b 2 + ba ab + a 2(a + b ) ⋅ ( y + a − b ) = y + a − b=ab ⋅ (a + b )ab4)=y −ba 2 − ab−y−aab − b 2=y −by−aby − b 2 − ay + a 2−==a ⋅ (a − b ) b ⋅ (a − b )ab ⋅ (a − b )(b − a ) ⋅ ( y − b − a ) = b + a − yab ⋅ (a − b )ab1a +1− b=;1+ b1− b1− b2212+ x −3x −1+= 2= 22) 2x+3x −9x −9x −9468.

1)3)4)a2+5+ p2p 2 − 36−5+ p2 − p2 + 6p5+6pp== 226+ pp − 36p − 362x5 x − 2 2 x 2 + 8 x − 5 x + 2 2 x 2 + 3x + 2− 2==x − 4 x − 16x 2 − 16x 2 − 16yy−zz+=n−2 2−n n−2p + 2q 5q − 2 p p + 2q − 2 p + 5q 7q − p=−=2)3p − q q − 3p3p − q3p − q469. 1)2m7n − 4 −2m − 5n + 3 + 7 n − 4 2n − 2m − 1−1+==3 − 5n5n − 35n − 35n − 33a5 ⋅ (a − 10 ) 20 − 8b − 3a − 5a + 50 70 − 8a − 8b4) 4 −==+5 − 2b2b − 55 − 2b5 − 2b3)2x5 x − 2 2 x 2 + 8 x + 5 x − 2 2 x 2 + 13x − 2==−x − 4 16 − x 2x 2 − 16x 2 − 1612n − 5612n − 5 − 42 − 6n 6n − 472) 2= 2+=n − 49 7 − nn 2 − 49n − 49470. 1)1013)=4)471. 1)2)3)4)c 2 − 8 16c − 2c 3 3c 2 − 24 − 2c 2 + 16c − 16c + 2c 2−==2c + 3 9 − 4c 29 − 4c 23 ⋅ c 2 − 249 − 4c 221y 2 + 11 − 9 y232a3a + 6 + 2a5a + 6=+=a + 2 (a + 2 )2(a + 2)2 (a + 2)2a7(a − b )257 + 5a − 5b;=b−a(a − b )2−74 − 7n + 7m=n−m(n − m )2(m − n )2aa2;=a −1 a −1bb 2 − 2b − b b 2 − 3b==b−2b−2b−23) c + 1 −=4a + 12a + 4 13a + 4==3a + 1(3a + 1)2 (3a + 1)2−42) b −473.

1)+(3a + 1)2472. 1) a +4)21y 2 + 1 + 32 + y 24 y 2 + y + 1y==3y −11 − 9 y21 − 9 y2−c2c2 − 1 − c21==−c −1c −1c −1a2a2 − a2 + 11− a +1 ==a +1a +1a +17a − 12a 2 + 6a+5 − 3aa2 − 9=7a − 15 − 3a+=2a ⋅ (a + 3) (a + 3) ⋅ (a − 3)7 a 2 − a − 21a + 3 + 10a − 6a 2(2a ⋅ a 2 − 9)=a 2 − 12a + 32a ⋅ (a − 3)(a + 3)68x22x2x − 2 y + 2x+ 2=+==2)23x + 3 y 4 x − 4 yx + y (x − y ) ⋅ (x + y )x2 − y2=1024x − 2 yx2 − y 23a − b3a − ba−=a −ba − ab (a − b ) ⋅ (a + b ) a ⋅ (a − b )3a − b − a − b 2a − 2b2= 2==2(a − b ) ⋅ (a + b ) a − b a + b3)4)=5)=6)=223a24a − 12−−a=2a +12a + a23aa +1−=(2a − 1) ⋅ (2a + 1) a ⋅ (2a + 1)=23a − 2a − 2a + a + 1()2a ⋅ 4a − 1b −1(b + 3)2−b2b −9==(b + 3)2(b + 3)2 ⋅ (b − 3)2a −4−a(a − 2)2=()a ⋅ 4a 2 − 1b −1b 2 − b − 3b + 3 − b 2 − 3ba −3a2 − a + 1=−b(b − 3) ⋅ (b + 3)=3 − 7b(b + 3)2 ⋅ (b − 3)a −3−a(a − 2) ⋅ (a + 2) (a − 2)2a 2 − 3a − 2a + 6 − a 2 − 2a(a − 2)2 ⋅ (a + 2)==6 − 7a(a − 2)2 ⋅ (a + 2)7816b7 a − 7b + 8a + 8b − 16b+−==a + b a − b a 2 − b2a 2 − b215a − 15b15==(a − b ) ⋅ (a + b ) a + b474.

1)a = 0,05; b = −0,04:2)1515== 1500(0,05 − 0,04) 0,013212−9 + 3a + 2a + 6 − 12 −15 + 5a5−− 2===22a +3 3−a a −9a+3−9+ a−9+ a5= −1−8+36x346 x − 3x − 3 y − 4 x + 4 y3) 2−−==2xyxy−+x −yx2 − y2a = −8:=−x + y1=−(x − y ) ⋅ (x + y ) x + yx=31; y=− :721−2115=−= −23 188−7 2110343−18 − 8a + 12 + 6a + 9+==2 a + 3 2a − 39 − 4a4a 2 − 93 − 2a1=−=(2a − 3) ⋅ (2a + 3) 2a + 3184)2−a = −0,6:2y + 8475. 1)2)y2 − 4 y + 44 + 6x1 + 6x + 9x225 − 10a + a=4)=−72 y + 8 − 7 y + 14 22 − 5 y==y−2( y − 2)2( y − 2)2−24 + 6x − 6x − 22==3x + 1(1 + 3x )2(1 + 3x )223)115=−=−2 ⋅ (− 0,6 ) + 31,89−2−102a − 2510 + 2a + 50 − 10a(5 − a ) ⋅ (5 + a )21x2 − 6 x + 9+1==2(5 − a )21==a −1a2 + 4−12a + a +1=(x2−9a −1)23x − 1 5 x − 2−=22312 x + 9 x − 3 − 10 x + 4 = 1211x = 11x =14z3 z − 17 z + 54)− 17 +=34216 z − 204 + 9 z − 51 = 6 z + 3019 z = 2852) 2 x +z = 15a +1− a +13=2 x 2 + 184 x − 3 5 − 2 x 3x − 4−−=5;23312 x − 9 − 10 + 4 x − 6 x + 8 = 30 ;10 x − 11 = 30 ;x = 4,1 ;8x + 7 5x − 23 − 2x3);−= 3−62416 x + 14 − 30 x + 12 = 36 − 9 + 6 x ;20 x = 1 ;1x=−;2031+(x + 3)2 (x − 3)2 (x + 3)2(x − 3)2 ⋅ (x + 3)2=23a −11a 2 + 4 − a 2 + 2a − 42a−== 32) 33a +8 a +2a +8a +8104=(5 − a )2 ⋅ (5 + a )x2 + 6 x + 9 + x2 − 6 x + 9a +110(5 − a ) ⋅ (5 + a )60 − 8a476.

1)477. 1)+3)4)478. 1)a+b2a − ab + b2=2)==−1m 2 − 3m + 9 − m 2 − 3m − 96m=− 3=3m−3m − 27m − 27m 3 − 278a 23a −1+a +12a + a +13c − c + 8−3c −1=8a 2 + a 2 − 13a −1c −1=9a 2 − 13a −12=1−cc + c +13c − c + 8 − c 2 + 2c − 1 − 2c 2 − 2c − 2c 3 −1a−b2n+1na +ba n + bna2n−c+5=c 3 −1n n+ 2a b + b2nn+−1na −b1na +bnn−=5−cc 3 −11 + a n − bn − a n − bna1an=2n−b(a n ⋅ a n + bna n − bna n ⋅ a n + bn2na n + bn + a n + bn(ana 2 n + b n a n + a 2 n + a nb n − a 2 n − 2 a n b n − b 2 n(=1−1 + 59282==1271919−1812n9 ⋅ 4 −1=58 −1; a = 2:+221c =1 :2479.

1)1a 2 + 2ab + b 2 − a 2 + ab − b 23ab== 3 3a+ba 3 + b3a +bm 2 − 3m + 922)−)2+b=)n 2=−1 − 2b na 2n − b2n1a 2n − b2n(=ana n ⋅ a n + bn)2=)§ 27. Умножение и деление алгебраических дробей85 72⋅= 5 ⋅ 3 = 15 ;24 1772 ⋅ 7 143) 50 ⋅;==6252525480. 1)481. 1)3)256 ⋅ 13 4 ⋅14==169 ⋅ 64 13 ⋅ 1 1355⋅34)⋅ 39 == 7,52622)a3b c 2 bc⋅=;c a4a2)2a2a ⋅ 6c 4ac;⋅ 6c ==3b3bb4) 14a 2 ⋅m2n2 k 3m2n2k 3 k 2⋅ 3 3 ==kmnmnkm3n3b27c 3=2a 2b 2c31058 8: = 1;17 173a m 3an3);: =7b n 7bma a: =1b bc 3a 5bc4): =2d 5b 6ad482. 1)5)2)2a a 2 2a ⋅ bc 2c:==;3b bc 3b ⋅ a 2 3a44:5 =;13658 12 ⋅ 9 2713) 12: === 13 ;9822483.

1)6)5m 10m35m ⋅ n1:= 2=23nnn ⋅ 10m2nm 22)aa:c =bbc4) a :b ac=c b2225a 2 ⋅ 14b 22⎛ 5a ⎞ 14b==⎟ ⋅3237a49b ⋅ 25a⎝ 7b ⎠ 25a484. 1) ⎜3⎛ 3a 2 ⎞ 16b3 27 a 6 ⋅ 16b3 9a 2 ⋅ 2 18a 2⎟ ⋅2) ⎜===434⎜ 2b ⎟⎝⎠1⋅ 78b ⋅ 21a21a72a 2b 2 ⋅ acd a3b2⎛ ab ⎞=⎟ ⋅ acd =cdc 2d 2⎝ cd ⎠3) ⎜2abc 2 ⋅ a 2b 2 a3b3⎛ ab ⎞= 2⎟ =c 2d 2d⎝ cd ⎠4) abc 2 ⋅ ⎜485.

1)2)8a 2b 36c3 32c 2⋅=;9c 5a 3b5a7b 4535b 4 c49c y 18c y22=7b 4 ⋅18c 4 y 2549c y ⋅ 35b c=2y2y=c ⋅ 5c 5c 23)16 x y 10 xy16 x 2 y ⋅ 21z 2 8 x ⋅ 3z 24 xz:===27z21z10 xy3 ⋅ 7 z5y25 y24)46d 3c 23dc 2 46d 3c ⋅ 5a3 2d 2a 2==:3c15a5a 315a ⋅ 23dc 25)18m3n5 2m3n318m3n5=: 9n 2 =7k7k7 k ⋅ 9n 26) 24k 2 :106:3( )12m 4k 211 p3n=24k 2 ⋅ 11 p3n12m4k 2=22 p3nm47− x a −b a −b;=⋅a+b 7− x a+b2)x − y 4b4b 2b⋅==2 a x − y 2aa3)c+dcc+d:=;c−d c−dc4)a − b a − b (a − b ) ⋅ 6b 2:== 3b2b 6b 22b ⋅ (a − b )5)a 2 − ab b 2 a ⋅ (a − b ) b 2: =⋅= (a − b ) ⋅ bbaba6)ab + b 2 b 2 b ⋅ (a + b ) ⋅ 3a a ⋅ (a + b ):==93a3b9⋅b2486. 1)487.

1)2)3)=1− a3b2⋅b31− a=2(1 − a ) ⋅ b = b3 ⋅ (1 − a ) ⋅ (1 + a ) 3 ⋅ (1 + a )15m35m ⋅ (m − n )1==232m−nm −n15m ⋅ (m − n ) ⋅ (m + n ) 3m ⋅ (m + n )5m:23 ⋅ (x + y )2(24y ⋅ x + y2)⋅x2 + y22x −y2=(3 ⋅ (x + y ) ⋅ x 2 + y 2())4 y ⋅ x + y ⋅ (x − y ) ⋅ (x + y )222=34 ⋅ y ⋅ (x − y )2( )= 53 ⋅ (a − b )( )6,253a3a ⋅ (a − b )a −ba488.

1); a = 2,5 : −= −1,25⋅=−=−3a + 3b 5b − 5a5515 ⋅ (a − b )5 x − 5 y 3x + 3 y− 5 ⋅ ( y − x ) ⋅ (x + y ) ⋅ 3(x + y )2)⋅=10 y − 10 x(x + y )⋅10( y − x) =x +y4)5 ⋅ (a − b )():(a − b )23 ⋅ a 2 + b2 a 2 + b2222=5 ⋅ (a − b ) ⋅ a 2 + b 23 ⋅ a 2 + b 2 ⋅ (a − b )222222=−222222222223 ⋅ (x + y )252x= ; y= :63⎛5− 3⋅⎜ +⎝622⎞⎟3⎠=9− 3⋅9= − = −2,252⋅64(− 5 + a ) ⋅ (3 + a )a 2 − 25 a + 5 (a − 5) ⋅ (a + 5) ⋅ (3 − a ) ⋅ (3 + a ):==−a ⋅ (a − 3) ⋅ (a + 5)aa 2 − 3a 9 − a 2a = 1:4 ⋅ 4 = 163)1074)3n 2 − 3m 2 6m − 6n − 3 ⋅ (m − n ) ⋅ (n + m ) ⋅ (n + p )n+m==−:n+ pn ⋅ (n + p ) ⋅ 6(m − n )2nn 2 + npm = −9; n = −3 :489.

1)a 2 + b23⋅2−x2 − y 24x + x y a −b(a4)(=−9 − 3 12== −22 ⋅ (− 3) − 6x− y(x ⋅ a 2 − b2+ b ⋅ (x − y ) ⋅ (x + y )22)(x2 ⋅ (x + y ) ⋅ a 2 − b2 ⋅ a 2 + b2)x− y) = x ⋅ (a22− b2x− y) ≠ x ⋅ (a2− b2)Равенство неверное.2)a 2 + b 2 a 4b − b51: 2= 222a − ab a b − aba − b2(a2)+ b 2 ⋅ ab(a − b )()(a(a − b ) ⋅ b a 2 + b 2 a 2 − b 2)= a12− b2Равенство верное.490. 1)2)3)4)(a − 5) ⋅ (a + 3)2 = 1a + 6a + 9 a − 25 (a + 3)2 ⋅ (a − 5)(a + 5) a + 5b 2 − 8b + 16 (b − 4)2 (b − 4)2 ⋅ (b − 3) ⋅ (b + 3): 2== b−3b+3b −9(b + 3) ⋅ (b − 4)2a 2 − 49a + b (a − 7 )(a + 7 ) ⋅ (a + b ) a + 7⋅==22 a−7a+ba + 2ab + b(a + b )2 ⋅ (a − 7 )22(a − 1) ⋅ (2a − 1) ⋅ (2a + 1) = (a − 1) ⋅ (2a − 1)a − 2a + 1 a − 1:=(2a + 1) ⋅ (a − 1)2a + 1 4 a 2 − 1a −52⋅(a + 3)22=3 ⋅ ( x − 11) 3 ⋅ (x + 1) 2 ⋅ (2 x − 5)=−4511165 ⋅ (x − 11) = 132 ⋅ (x + 1) − 40 ⋅ (2 x − 5)165 x − 1815 = 132 x + 132 − 80 x + 200113x = 2147 ; x = 192 ⋅ (5 x + 2)4 ⋅ (33 + 2 x ) 5 ⋅ (1 − 11x )2)−1 =−95910 ⋅ (5 x + 2 ) − 45 = 36 ⋅ (33 + 2 x ) − 25 ⋅ (1 − 11x )50 x + 20 − 45 = 1188 + 72 x − 25 + 275 x297 x = −1188 ; x = −4491.

1)1083)8 ⋅ (x + 10)1 7 x 2 ⋅ (11x − 5)− 24 =−152 10516 ⋅ (x + 10 ) − 49 ⋅ 15 = 21x − 12 ⋅ (11x − 5)16 x + 160 − 735 = 21x − 132 x + 60127 x = 635 ; x = 54)2 ⋅ (x − 4 ) 3x + 13 3 ⋅ (2 x − 3)+=−738580 ⋅ (x − 4) + 15 ⋅ (3 x + 13) = 72 ⋅ (2 x − 3) − 84080 x − 320 + 45 x + 195 = 144 x − 216 − 840 ; 19 x = 931 ; x = 49492. a ≠ 0; b ≠ 0; a ≠ b; a ≠ −ba + b a 2 − b2=;xa(a + b ) ⋅ a = a ;x=(a + b )(a − b ) a − bxab=a 2 − b 2 a 2 − ab(a − b )(a + b ) ⋅ ab = b ⋅ (a + b )x=a ⋅ (a − b )2)1)aa−bОтвет: x =3)Ответ: x = b ⋅ (a + b )a 2 − 2ab + b 2 a 2 − b 2;=bxx=b ⋅ (a − b )(a + b )=(a − b )2Ответ: x =b ⋅ (a + b )a −bab 2 − b34)3a b − ab=2)2a + 2ab + b 2b ⋅ (a − b )xb ⋅ (a + b )=;a−bab ⋅ a 2 − b 2(a + b )22x=()b ⋅ (a − b ) ⋅ (a + b )22(2ab ⋅ a − bОтвет: x =493. 1)x=3(2)=b ⋅ (a + b )ab ⋅ (a + b )a)(a − b )2 ⋅ a3 + b3 =a 2 − 2ab + b 2 8a − 8b:=a 2 − ab + b 2 a 3 + b3 8(a − b ) ⋅ a 2 − ab + b 2(a − b ) ⋅ (a + b ) ⋅ (a((22− ab + b8 ⋅ a − ab + b2a + 2ab + b2a + ab + b22(a + b ) ⋅ (a − b )=⋅2)2)= a2−b8)2())(a + b )2 ⋅ (a − b ) ⋅ a 2 + ab + b2 =a −b=7 a + 7ba 2 + ab + b 2 ⋅ 7(a + b )33(71093)=4)=494.

1)n3 − m3n 2 + nm + m 2:n 2 − m 2 n 2 + 2nm + m 2=(n − m )⋅ (n 2 + nm + m 2 )⋅ (n + m )2(n + m )⋅ (n − m )(n 2 + nm + m 2 )m 2 + 2mn + n 23p +c3m+n(22 p − pc + c 2a 2n − b 2na2n+b⋅2n⋅(m + n )2 ⋅ ( p + c )p+c==2m + 2n ( p + c ) ⋅ p 2 − pc + c 2 ⋅ 2(m + n )(2n2n2nn n− 2a b + b4n4nnn 22nn()⋅ (aa 4n − b 4na))n 2nnn 22n= an + bn2n(a − b )⋅ (a − b ) = (a − b(a + b )⋅ (a − b )(a(a + b ) ⋅ (a − b ) = (a + b )=(a − b )2n= n+m2n2nn 22n+b2n− b2n)⋅ (an))⋅ (a2−b2n)n 2n 2nОтвет: верно.2)(xnx4n−y)24n:x 2n − y 2nx2n+y2n=(x1n− yn)2( x n + y n ) 2 ⋅ ( x 2n + y 2n )=− y 2n ) ⋅ ( x 2n + y 2n ) ⋅ ( x 2n − y 2n )( x 2n=+ yn(x n + y n ) 2nn 2nn 2(x − y ) ⋅ (x + y )Ответ: верно.=1n(x − y n ) 2§ 28.